RD SHARMA Solutions for Class 10 Maths Chapter 3 - Pairs of Linear Equations in Two Variables

Chapter 3 - Pairs of Linear Equations in Two Variables Exercise Ex. 3.1

Question 1
Akhila went to a fair in her village. She wanted to enjoy rides on the Giant Wheel and play Hoopla (a game in which you throw a rig on the items kept in the stall, and if the ring covers any object completely you get it). The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. Each ride costs Rs 3, and a game of Hoopla costs Rs 4. If she spent Rs 20 in the fair, represent this situation algebraically and graphically.
Solution 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 2
Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be." (Isn' this interesting?) Represent this situation algebraically and graphically.
Solution 2
Let the present age of Aftab and his daughter be x and y respectively.

Seven years ago,
Age of Aftab = x - 7
Age of his daughter = y - 7

According to the given condition,

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables 
Three years hence,
Age of Aftab = x + 3
Age of his daughter = y + 3

According to the given condition,

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables 

Thus, the given conditions can be algebraically represented as:
x - 7y = -42
x - 3y = 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables 
Three solutions of this equation can be written in a table as follows:
x -7 0 7
y 5 6 7


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables 

Three solutions of this equation can be written in a table as follows:
x 6 3 0
y 0 -1 -2


The graphical representation is as follows:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Concept insight: In order to represent a given situation mathematically, first see what we need to find out in the problem. Here, Aftab and his daughter's present age needs to be found so, so the ages will be represented by variables x and y. The problem talks about their ages seven years ago and three years from now. Here, the words 'seven years ago' means we have to subtract 7 from their present ages, and 'three years from now' or 'three years hence' means we have to add 3 to their present ages. Remember in order to represent the algebraic equations graphically the solution set of equations must be taken as whole numbers only for the accuracy. Graph of the two linear equations will be represented by a straight line.
Question 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 5(i)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 5(i)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 5(ii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 5(ii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 5(iii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 5(iii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 6(i)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 6(i)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 6(ii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 6(ii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 6(iii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 6(iii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 7
The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.
Solution 7
Let the cost of 1 kg of apples and 1 kg grapes be Rsx and Rsy.
The given conditions can be algebraically represented as:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Three solutions of this equation can be written in a table as follows:


x
50 60 70
y 60 40 20


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Three solutions of this equation can be written in a table as follows:


x
70 80 75
y 10
-10
0


The graphical representation is as follows:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Concept insight: cost of apples and grapes needs to be found so the cost of 1 kg apples and 1 kg grapes will be taken as the variables. From the given conditions of collective cost of apples and grapes, a pair of linear equations in two variables will be obtained. Then, in order to represent the obtained equations graphically, take the values of variables as whole numbers only. Since these values are large so take the suitable scale.

Chapter 3 - Pairs of Linear Equations in Two Variables Exercise Ex. 3.2

Question 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 5
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 5
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 6
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 6
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 7
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 8
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 8
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 9
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 9
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 10
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 10
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 11
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 11
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 12
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 12
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Since, the graph of the two lines coincide, the given system of equations have infinitely many solutions.
Question 13
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 13
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 14
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 14
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 15
Show graphically that each one of the following systems of equations is in-coinsistent (i.e. has no solution):

3x - 5y = 20

6x - 10y = - 40
Solution 15
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 16
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 16
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 17
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 17
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 18
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 18
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 19(i)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 19(i)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 19(ii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 19(ii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 20
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 20
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 21(i)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 21(i)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 21(ii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 21(ii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 22(i)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 22(i)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 22(ii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 22(ii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 22(iii)
Solve graphically each of the following systems of linear equations. Also find the coordinates of the points where the lines meet axis of y.

2x + y - 11 = 0

x - y - 1 = 0
Solution 22(iii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 22(iv)
Solve graphically each of the following systems of linear equations. Also find the coordinates of the points where the lines meet axis of y.

x + 2y - 7 = 0

2x - y - 4 = 0
Solution 22(iv)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 22(v)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 22(v)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 22(vi)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 22(vi)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 23(i)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 23(i)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 23(ii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 23(ii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 23(iii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 23(iii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
 
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 28(i)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 28(i)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 28(ii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 28(ii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 28(iii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 28(iii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 28(iv)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 28(iv)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 32

Draw the graphs of the equations 5x - y = 5 and 3x - y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis. Calculate the area of the triangle so formed.

Solution 32

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Three solutions of this equation can be written in a table as follows:

x 0 1 2
y -5 0 5


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

x 0 1 2
y -3 0 3


The graphical representation of the two lines will be as follows:

 


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
It can be observed that the required triangle is Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two VariablesABC.
The coordinates of its vertices are A (1, 0), B (0, -3), C (0, -5).

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Concept insight: In order to find the coordinates of the vertices of the triangle so formed, find the points where the two lines intersects the y-axis and also where the two lines intersect each other. Here, note that the coordinates of the intersection of lines with y-axis is taken and not with x-axis, this is because the question says to find the triangle formed by the two lines and the y-axis.

Question 33

Form the pair of linear equations in the following problems, and find their solutions graphically.

(i)  10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
(ii)  5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.

(iii) Champa went to a 'Sale' to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, "The number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased". Help her friends to find how many pants and skirts Champa a bought.

Solution 33

(i) Let the number of girls and boys in the class be x and y respectively.
According to the given conditions, we have:
x + y = 10
x - y = 4
x + y = 10 Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables x = 10 - y
Three solutions of this equation can be written in a table as follows:

x 4 5 6
y 6 5 4



x - y = 4 Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables x = 4 + y
Three solutions of this equation can be written in a table as follows:

x 5 4 3
y 1 0 -1



The graphical representation is as follows:
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
From the graph, it can be observed that the two lines intersect each other at the point (7, 3).
So, x = 7 and y = 3.

Thus, the number of girls and boys in the class are 7 and 3 respectively.


(ii)    Let the cost of one pencil and one pen be Rs x and Rs y respectively.

According to the given conditions, we have:
5x + 7y = 50
7x + 5y = 46
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Three solutions of this equation can be written in a table as follows:

x 3 10 -4
y 5 0 10



Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Three solutions of this equation can be written in a table as follows:

x 8 3 -2
y -2 5 12



The graphical representation is as follows:
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

From the graph, it can be observed that the two lines intersect each other at the point (3, 5).
So, x = 3 and y = 5.

Therefore, the cost of one pencil and one pen are Rs 3 and Rs 5 respectively.



(iii)

Let us denote the number of pants by x and the number of skirts by y. Then the equations formed are:

y = 2x - 2 ...(1)

and y = 4x - 4 ...(2)

Let us draw the graphs of Equations (1) and (2) by finding two solutions for each of the equations.

They are given in Table

x 2 0
y = 2x - 2 2 -2



x 0 1
y = 4x - 4 -4 0

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables



Plot the points and draw the lines passing through them to represent the equations, as shown in fig.,

The two lines intersect at the point (1,0). So, x = 1, y = 0 is the required solution of the pair of linear equations, i.e., the number of pants she purchased is 1 and she did not buy any skirt.

Concept insight: Read the question carefully and examine what are the unknowns. Represent the given conditions with the help of equations by taking the unknowns quantities as variables. Also carefully state the variables as whole solution is based on it. On the graph paper, mark the points accurately and neatly using a sharp pencil. Also, take at least three points satisfying the two equations in order to obtain the correct straight line of the equation. Since joining any two points gives a straight line and if one of the points is computed incorrect will give a wrong line and taking third point will give a correct line. The point where the two straight lines will intersect will give the values of the two variables, i.e., the solution of the two linear equations. State the solution point.

Question 34(i)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 34(i)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 34(ii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 34(ii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 36

Given the linear equation 2x + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:

(i) Intersecting lines

(ii) parallel lines

(iii) Coincident lines

Solution 36

(i) For the two lines a1x + b1x + c1 = 0 and a2x + b2x + c2 = 0, to be intersecting, we must have
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
So, the other linear equation can be 5x + 6y - 16 = 0
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables 
(ii)  For the two lines a1x + b1x + c1 = 0 and a2x + b2x + c2 = 0, to be parallel, we must have
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
So, the other linear equation can be 6x + 9y + 24 = 0,
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
(iii)  For the two lines a1x + b1x + c1 = 0 and a2x + b2x + c2 = 0 to be coincident, we must have
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
So, the other linear equation can be 8x + 12y - 32 = 0,
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Concept insight: In order to answer such type of problems, just remember the conditions for two lines to be intersecting, parallel, and coincident. This problem will have multiple answers as their can be many equations satisfying the required conditions.

Question 37(i)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 37(i)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 37(ii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 37(ii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 38

Graphically, solve the following pair of equations:

 

2x + y = 6

2x - y + 2 = 0

Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.

Solution 38

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

The lines AB and CD intersect at point R(1, 4). Hence, the solution of the given pair of linear equations is x = 1, y = 4.

 

From R, draw RM X-axis and RN Y-axis.

Then, from graph, we have

RM = 4 units, RN = 1 unit, AP = 4 units, BQ = 4 units

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 39

Determine, graphically, the vertices of the triangle formed by the lines y = x, 3y = x, x + y = 8.

Solution 39

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

From the graph, the vertices of the triangle AOP formed by the given lines are A(4, 4), O(0, 0) and P(6, 2).

Question 40

Draw the graph of the equations x = 3, x = 5 and 2x - y - 4 = 0. Also, find the area of the quadrilateral formed by the lines and the x-axis.

Solution 40

The graph of x = 3 is a straight line parallel to Y-axis at a distance of 3 units to the right of Y-axis.

 

The graph of x = 5 is a straight line parallel to Y-axis at a distance of 5 units to the right of Y-axis.

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 41

Draw the graphs of the lines x = -2, and y = 3. Write the vertices of the figure formed by these lines, the x-axis and the y-axis. Also, find the area of the figure.

Solution 41

The graph of x = -2 is a straight line parallel to Y-axis at a distance of 2 units to the left of Y-axis.

 

The graph of y = 3 is a straight line parallel to X-axis at a distance of 3 units above X-axis.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 42

Draw the graphs of the pair of linear equations x - y + 2 = 0 and 4x - y - 4 = 0. Calculate the area of the triangle formed by the lines so drawn and the x-axis.

Solution 42

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Chapter 3 - Pairs of Linear Equations in Two Variables Exercise Ex. 3.3

Question 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 5
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 6
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 6
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 7
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 7
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 8
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 9
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 9
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 10
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 10
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 12
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 12
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 13
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 13
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 14
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 14
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 15
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 15
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 16
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 16
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 25

Solve the following systems of equation:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 32

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 32

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 33

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 33

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 34

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 34

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 36

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 36

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 38

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 38

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 39

Solve the pair of equations:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 39

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 41

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 41

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 42

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 42

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 43

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 43

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 44

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 44

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 45

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 45

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 46

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 46

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 47

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 47

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 48

Solve the following systems of equation:

 

21x + 47y = 110

47x + 21y = 162

Solution 48

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 49

If x + 1 is a factor of 2x3 + ax2 + 2bx + 1, the find the values of a and b given that 2a - 3b = 4.

Solution 49

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 50

Find the solution of the pair of equations Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables and Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables. Hence, find λ, if y = λx + 5.

Solution 50

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 51

Find the values of x and y in the following rectangle.

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 51

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 52

Write an equation of a line passing through the point representing solution of the pair of linear equations x + y = 2 and 2x - y = 1. How many such lines can we find?

Solution 52

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 53

Write a pair of linear equations which has the unique solution x = -1, y = 3. How many such pairs can you write?

Solution 53

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Chapter 3 - Pairs of Linear Equations in Two Variables Exercise Ex. 3.4

Question 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 5
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 5
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 6
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 6
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 7
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 7
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 8
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 8
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 14

Solve each of the following systems of equations by the method of cross-multiplication:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 15
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 15
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 16
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 16
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 17
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 17
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 18
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 18
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 19
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 19
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 20
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

 

Question 21
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 21
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 23
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 23
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 24
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 25
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 25
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 27
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 27
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 28
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 28
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Chapter 3 - Pairs of Linear Equations in Two Variables Exercise Ex. 3.5

Question 1

Determine whether the following system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:

x - 3y = 3

3x - 9y = 2

Solution 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 2

Determine whether the following system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:

2x + y = 5

4x + 2y = 10

Solution 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 3

Determine whether the following system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:

3x - 5y = 20

6x - 10y = 40

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 4

Determine whether the following system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:

x - 2y = 8

5x - 10y = 10

Solution 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 5

Find the value of k for which the following system of equations has a unique solution:

kx + 2y = 5

3x + y = 1

Solution 5
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 6
Find the value of k for which the following system of equations has a unique solution:

4x + ky + 8 = 0

2x + 2y + 2 = 0
Solution 6
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 7

Find the value of k for which the following system of equations has a unique solution:

4x - 5y = k

2x - 3y = 12

Solution 7
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 8

Find the value of k for which the following system of equations has a unique solution:

x + 2y = 3

5x + ky + 7 = 0

Solution 8
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 9

Find the value of k for which the following systems of equations have infinitely many solutions:

2x + 3y - 5 = 0

6x + ky - 15 = 0

Solution 9
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 10

Find the value of k for which the following systems of equations have infinitely many solutions:

4x + 5y = 3

kx + 15y = 9

Solution 10
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 11

Find the value of k for which the following systems of equations have infinitely many solutions:

kx - 2y + 6 = 0

4x - 3y + 9 = 0

Solution 11
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 12

Find the value of k for which the following systems of equations have infinitely many solutions:

8x + 5y = 9

kx + 10y = 18

Solution 12
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 13

Find the value of k for which the following systems of equations have infinitely many solutions:

2x - 3y = 7

(k + 2)x - (2k + 1)y = 3(2k - 1)

Solution 13
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 14

Find the value of k for which the following systems of equations have infinitely many solutions:

2x + 3y = 2

(k + 2)x + (2k + 1)y = 2(k - 1)

Solution 14
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 15

Find the value of k for which the following systems of equations have infinitely many solutions:

x + (k + 1)y = 4

(k + 1)x + 9y = (5k + 2)

Solution 15
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 16

Find the value of k for which the following systems of equations have infinitely many solutions:

kx + 3y = 2k + 1

2(k + 1)x + 9y = 7k + 1

Solution 16
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 17

Find the value of k for which the following systems of equations have infinitely many solutions:

2x + (k - 2)y = k

6x + (2k - 1)y = 2k + 5

Solution 17
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 18

Find the value of k for which the following systems of equations have infinitely many solutions:

2x + 3y = 7

(k + 1)x + (2k - 1)y = 4k + 1

Solution 18
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 19

Find the value of k for which the following systems of equations have infinitely many solutions:

2x + 3y = k

(k - 1)x + (k + 2)y = 3k

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 20
Find the value of k for which the following system of equations has no solution:

kx - 5y = 2

6x + 2y = 7
Solution 20
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 21
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 21
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 22
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 22
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 23
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 23
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 24
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 24
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 25

Find he value of k for which of the following system of equation has no solution:

 

kx + 3y = k - 3

12x + ky = 6

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 26
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 26
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 27
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 27
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 28
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 28
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 29
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 29
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 30
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 31
For what value of k, the following system of equations will represent the coincident lines?

x + 2y + 7 = 0

2x + ky + 14 = 0
Solution 31
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 32
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 32
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 33
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 33
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 34
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 34
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 35
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 36 (i)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 36 (i)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 36 (ii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 36 (ii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 36 (iii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 36 (iii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 36 (iv)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 36 (iv)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 36 (v)

Find the values of a and b for which the following system of equations has infinitely many solutions:

2x + 3y = 7

(a - b) x + (a + b)y = 3a + b - 2

Solution 36 (v)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 36 (vi)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 36 (vi)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 36 (vii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 36 (vii)
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 36(viii)

Find the values of a and b for which the following system of equations has infinitely many solutions:

 

x + 2y = 1

(a - b)x + (a + b)y = a + b - 2

Solution 36(viii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 36(ix)

Find the values of a and b for which the following system of equations has infinitely many solutions:

 

2x + 3y = 7

2ax + ay = 28 - by

Solution 36(ix)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 37(i)

For which value(s) of λ, do the pair of linear equations λx + y = λ2 and x + λy = 1 have no solution?

Solution 37(i)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 37(ii)

For which value(s) of λ, do the pair of linear equations λx + y = λ2 and x + λy = 1 have infinitely many solutions?

Solution 37(ii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 37(iii)

For which value(s) of λ, do the pair of linear equations λx + y = λ2 and x + λy = 1 have a unique solution?

Solution 37(iii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Chapter 3 - Pairs of Linear Equations in Two Variables Exercise Ex. 3.6

Question 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 5
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 5
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 6
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 6
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 7

Jamila sold a table and a chair for Rs.1050, thereby making a profit of 10% on a table and 25% on the chair. If she had taken profit of 25% on the table and 10% on the chair she would have got Rs.1065. Find the cost price of each.

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 8

Susan invested certain amount of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. She received Rs.1860 as annual interest. However, had she interchanged the amount of investment in the two schemes, she would have received Rs.20 more as annual interest. How much money did she invest in each scheme?

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 9

The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, he buys 3 bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 10

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs. 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 11

The cost of 4 pens and 4 pencils boxes is Rs.100. Three times the cost of a pen is Rs.15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box.

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 12

One says, "Give me a hundred, friend! I shall then become twice as rich as you". The other replies, "If you give me ten, I shall be six times as rich as you". Tell me what is the amount of their (respective) capital?

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 13

A and B each have a certain number of mangoes. A says to B, "if you give 30 of your mangoes, I will have twice as many as left with you. "B replies, "if you give me 10, I will have thrice as many as left with you. "How many mangoes does each have?

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 14

Vijay had some bananas, and he divided them into two lots A and B. He sold first lot at the rate of Rs.2 for 3 bananas and the second lot at the rate of Rs.1 per banana and got a total of Rs.400. If he had sold the first lot at the rate of Rs.1 per banana and the second lot at the rate of Rs.4 per five bananas, his total collection would have been Rs.460. Find the total number of bananas he had.

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Chapter 3 - Pairs of Linear Equations in Two Variables Exercise Ex. 3.7

Question 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 5
The sum of two-digit number and the number formed by reversing the order of digits is 66. If the two digits differ by 2, find the number. How many such numbers are there?
Solution 5
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 7
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 7
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 8
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 8
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 9
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 9
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 10
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 10
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 11
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 11
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 12
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 12
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 13
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 13
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 14
The sum of digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
Solution 14
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 15
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 15
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 16

Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5. Find the numbers.

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 17

A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Chapter 3 - Pairs of Linear Equations in Two Variables Exercise Ex. 3.8

Question 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 2
A fraction becomes 9/11 if 2 is added to both numerator and the denominator. If 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.
Solution 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 4
If we add 1 to the numerator and subtract 1 from the denominator, a fraction becomes 1. It also becomes 1/2 if we only add 1 to the denominator. What is the fraction?
Solution 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 5

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 6
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 6
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 7
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 7
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 8
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 8
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 9
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 9
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Chapter 3 - Pairs of Linear Equations in Two Variables Exercise Ex. 3.9

Question 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 3

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 5
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 5
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 6
The present age of a father is three more than three times the age of the son. Three years hence father's age will be 10 years more than twice the age of the son. Determine their present ages.
Solution 6
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 7
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 7
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 8
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 8
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 9
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 9
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 11

The ages of two friends Ani and Biju differ by 3 years. Ani's father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differs by 30 years. Find the ages of Ani and Biju.

Solution 11

The difference between the ages of Ani and Biju is given as 3 years. So, either Biju is 3 years older than Ani or Ani is 3 years older than Biju.

Let the age of Ani and Biju be x years and y years respectively.
Age of Dharam = 2 × x = 2x years
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Case I: Ani is older than Biju by 3 years
x - y = 3        ... (1)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
4x - y = 60     ....(2)

Subtracting (1) from (2), we obtain:
 
3x = 60 - 3 = 57

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Age of Ani = 19 years
Age of Biju = 19 - 3 = 16 years

Case II: Biju is older than Ani by 3 years
y - x = 3        ... (3)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

4x - y = 60        ... (4)

Adding (3) and (4), we obtain:
3x = 63
x = 21

Age of Ani = 21 years
Age of Biju = 21 + 3 = 24 years

Concept Insight: In this problem, ages of Ani and Biju are the unknown quantities. So, we represent them by variables x and y. Now, note that here it is given that the ages of Ani and Biju differ by 3 years. So, it is not mentioned that which one is older. So, the most important point in this question is to consider both cases  Ani is older than Biju and  Biju is older than Ani. For second condition the relation  on the ages of Dharam and Cathy can be implemented . Pair of linear equations can be solved using a suitable algebraic method.

Question 12

Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now?

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 13

The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Chapter 3 - Pairs of Linear Equations in Two Variables Exercise Ex. 3.10

Question 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 3
The boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of stream and that of the boat in still water.
Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 6

A person rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of stream.

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 8
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 9
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 10
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 10

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables 

Question 11
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 12
Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.
Solution 12
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 13

A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 14
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 15
A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time.  Find the distance covered by the train.
Solution 15
Let the speed of the train be x km/h and the time taken by train to travel the given distance be t hours and the distance to travel be d km.
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Or, d = xt        ... (1)

According to the question,
 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

By using equation (1), we obtain:
3x - 10t = 30        ... (3)

Adding equations (2) and (3), we obtain:
x = 50
Substituting the value of x in equation (2), we obtain:
(-2) x (50) + 10t = 20
-100 + 10t = 20
10t = 120
t = 12
From equation (1), we obtain:
d = xt = 50 x 12 = 600

Thus, the distance covered by the train is 600 km.

Concept insight: To solve this problem, it is very important to remember the relation Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables. Now, all these three quantities are unknown. So, we will represent these

by three different
variables. By using the given conditions, a pair of equations will be obtained. Mind one thing that the equations obtained will not be linear. But they can be reduced to linear form by using the fact that Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables. Then two linear equations can be formed which can

be solved easily by elimination method.

Question 16
Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hours. What are the speeds of two cars?
Solution 16
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Chapter 3 - Pairs of Linear Equations in Two Variables Exercise Ex. 3.11

Question 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 1
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 2
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 4
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 5
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 5
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 6

ABCD is a cyclic quadrilateral such that Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two VariablesA = (4y + 20)o, Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two VariablesB = (3y - 5)o, Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two VariablesC = (-4x)o and Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two VariablesD = (7x + 5)o. Find the four angles.

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

We know that the sum of the measures of opposite angles in a cyclic quadrilateral is 180°.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two VariablesA + Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two VariablesC = 180
4y + 20 - 4x = 180
-4x + 4y = 160
x - y = -40            ... (1)
Also, Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two VariablesB + Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two VariablesD = 180
3y - 5 - 7x + 5 = 180
-7x + 3y = 180        ... (2)
Multiplying equation (1) by 3, we obtain:

3x - 3y = -120        ... (3)
Adding equations (2) and (3), we obtain:
-4x = 60
x = -15
Substituting the value of x in equation (1), we obtain:
-15 - y = -40
y = -15 + 40 = 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two VariablesA = 4y + 20 = 4(25) + 20 = 120o
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two VariablesB = 3y - 5 = 3(25) - 5 = 70o
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two VariablesC = -4x = -4(-15) = 60o
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two VariablesD = -7x + 5 = -7(-15) + 5 = 110o

Concept insight: The most important idea to solve this problem is by using the fact that the sum of the measures of opposite angles in a cyclic quadrilateral is 180o. By using this relation, two linear equations can be obtained which can be solved easily by eliminating a suitable variable.

Question 7
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 8
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 8
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 9
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 12
The car hire charges in a city comprise of fixed charges together with the charge for the distance covered. For a journey of 12 km, the charge paid is Rs 89 and for a journey of 20 km, the charge paid is Rs. 145. What will a person have to pay for travelling a distance of 30 km?
Solution 12
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 13
A part of monthly hostel charges in a college are fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days, he has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charge and the cost of food per day.
Solution 13
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 14
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Solution 14
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 15
The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
Solution 15
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 16
2 Women and 5 men can together finish a piece of embroidery in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the embroideery, and that taken by 1 man alone.
Solution 16
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
Question 17

Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many notes Rs 50 and Rs 100 she received.

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 21

The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row there would be 2 rows more. Find number of students in the class.

Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 22

One says, "Give me a hundred, friend! I shall then become twice as rich as you". The other replies, "If you give me ten, I shall be six times as rich as you". Tell me what is the amount of their (respective) capital?

Solution 22

Let the money with the first person and second person be Rs x and Rs y respectively.

According to the question,
x + 100 = 2(y - 100)
x + 100 = 2y - 200
x - 2y = -300        ... (1)

6(x - 10) = (y + 10)
6x - 60 = y + 10
6x - y = 70            ... (2)

Multiplying equation (2) by 2, we obtain:
12x - 2y = 140        ... (3)
Subtracting equation (1) from equation (3), we obtain:
11x = 140 + 300
11x = 440
x = 40
Putting the value of x in equation (1), we obtain:
40 - 2y = -300
40 + 300 = 2y
2y = 340
y = 170

Thus, the two friends had Rs 40 and Rs 170 with them.

Concept insight: This problem talks about the amount of capital with two friends. So, we will represent them by variables x and y respectively. Now, using the given conditions, a pair of linear equations can be formed which can then be solved easily using elimination method.

Question 23

A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby getting a sum of Rs.1008. If she had sold the saree at 10% profit and sweater at 8% discount, she would have got Rs.1028. Find the cost price of the saree and the list price (price before discount) of the sweater.

Solution 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 24

In a competitive examination, one mark is awarded for each correct answer while ½ mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?

Solution 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 25

A shopkeeper gives book on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid Rs.22 for a book kept for 6 days, while Rs.16 for the book kept for four days. Find the fixed charges and charge for each extraday.

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Chapter 3 - Pairs of Linear Equations in Two Variables Exercise 3.114

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

So, the correct option is (b).

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Chapter 3 - Pairs of Linear Equations in Two Variables Exercise 3.115

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 7

If   am ≠ bl, then the system of equations

ax + by = c

lx + my = n

(a)  has a unique solution        

(b) has no solution

(c) has infinite many solution    

(d) may or may not have a solution

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

So, the correct option is (a).

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

So, the correct option is (b).

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

So, the correct option is (a).

Question 10

If 2x-3y=7 and (a+b)x – (a+b-3)y = 4a+b represent coincident lines than a and b satisfy the equation

(a) a+5b=0    (b) 51+b=0    (c) a-5b=0     (d) 5a-b=0

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

So, the correct option is (c).

Question 11

If a pair of linear equations in two variables is consistent, then the lines represented by two equations are

(a) Intersecting             (b) parallel

(c) always coincident       (d) intersecting or coincident

Solution 11

Consistent solution means either linear equations have unique solutions or infinite solutions.

⇒ In case of unique solution; lines are intersecting

⇒ If solutions are infinite, lines are coincident.

So, lines are either intersecting or coincident

So, the correct option is (d).

Question 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

So, the correct option is (c).

Question 13

The area of the triangle formed by the lines

y=x,  x=6, and  y=0  is

(a) 36 sq. units      

(b) 18 sq. units

(c) 9 sq. units         

(d) 72 sq. units

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

So, the correct option is (b).

Question 14

If the system of equations 2x + 3y=5,  4x + ky =10 has infinitely many solutions, then k=

(a) 1     

(b) Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables    

(c) 3    

(d) 6

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

So, the correct option is (d).

Question 15

If the system of equations  kx - 5y = 2,  6x +2y=7 has no solution, then k=

(a) -10     

(b) -5      

(c) -6     

(d)-15

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

So, the correct option is (d).

Question 16

The area of the triangle formed by the lines

x = 3, y = 4 and x = y is

(a) Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables sq. unit    

(b) 1 sq. unit

(c) 2 sq. unit     

(d) None of these

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

So, the correct option is (a).

Chapter 3 - Pairs of Linear Equations in Two Variables Exercise 3.116

Question 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

The area of the triangle formed by the lines

2x + 3y = 12,     x – y – 1= 0  and x = 0

(a) 7 sq. units          

(b) 7.5 sq. units

(c) 6.5 sq. units        

(d) 6 sq. units   

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

So, the correct option is (b).

Question 18

The sum of the digits of a two digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is

 

  1. 25
  2. 72
  3. 63
  4. 36
Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 19

If x = a, y = b is the solution of the system of equations x - y = 2 and x + y = 4, then the values of a and b are, respectively

 

  1. 3 and 1
  2. 3 and 5
  3. 5 and 3
  4. -1 and -3
Solution 19

Since x = a and y = b is the solution of given system of equations x - y = 2 and x + y = 4, we have

a - b = 2 ….(i)

a + b = 4 ….(ii)

Adding (i) and (ii), we have

2a = 6 a = 3

b = 4 - 3 = 1

Hence, correct option is (a).

Question 20

For what value k, do the equations 3x - y + 8 = 0 and 6x - ky + 16 = 0 represent coincident lines?

 

  1. Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
  2. Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables
  3. 2
  4. -2
Solution 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables

Question 21

Aruna has only Rs.1 and Rs.2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs.75, then the number of Rs.1 and Rs.2 coins are, respectively

 

  1. 35 and 15
  2. 35 and 20
  3. 15 and 35
  4. 25 and 25
Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Pairs Of Linear Equations In Two Variables