Chapter 7 : Linear Equations in Two Variables - Rd Sharma Solutions for Class 9 Maths CBSE

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Chapter 7 - Linear Equations in Two Variables Excercise Ex. 7.1

Question 1

Solution 1


Question 2

Solution 2

Question 3

Solution 3

Chapter 7 - Linear Equations in Two Variables Excercise Ex. 7.2

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

If x = 1 and y = 6 is solution of the equation 8x - ay + a2= 0, find the value of a.

Solution 9

Question 10

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the follwoing equation: 5x - 2y = 10

Solution 10

Question 11

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equation: -4x + 3y = 12

Solution 11

Question 12

Solution 12

Chapter 7 - Linear Equations in Two Variables Excercise Ex. 7.3

Question 1

Solution 1


Question 2

Solution 2


Question 3

Solution 3


Question 4

Solution 4


Question 5

Solution 5


Question 6

Solution 6


Question 7

Solution 7


Question 8

Solution 8


Question 9

Solution 9

Question 10

Solution 10

Question 11

Plot the points (3,5) and (-1,3) on a graph paper and verify that the straight line passing through these points also passes through the point (1,4).

Solution 11

The given points on the graph:



It is dear from the graph, the straight line passing through these points also passes through the point (1,4).

Question 12

From the choices given below, choose the equation whose graph is given in fig.,

(i) y = x

(ii) x + y = 0

(iii) y = 2x

(iv) 2 + 3y = 7x

 

Solution 12



Question 13

From the choices given below, choose the equation whose graph is given in fig.,

(i) y = x + 2

(ii) y = x - 2

(iii) y = -x + 2

(iv) x + 2y = 6

 

Solution 13



Question 14

Solution 14

Question 15

Draw the graph of the equation 2x + 3y = 12. Find the graph, find the coordinates of the point.

(i) whose y-coordinate is 3.

(ii) whose x-coordinate is -3

Solution 15





Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

The sum of a two digit number and the number obtained by reversing the order of its digits is 121. If units and ten's digit of the number are x and y respectively, then write the linear equation representing the above statement.

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Draw the graph of y = |x|.

Solution 25

We have,

y = |X|                               ...(i)

Putting x = 0, we get y = 0

Putting x = 2, we get y = 2

Putting x = -2, we get y = 2

Thus, we have the following table for the points on graph of |x|.

x 0 2 -2
y 0 2 2



The graph of the equation y = |x|:

Question 26

Draw the graph of y = |x| + 2.

Solution 26

We have,

y = |x| + 2                                                  ...(i)

Putting x = 0, we get y = 2

Putting x = 1, we get y = 3

Putting x = -1, we get y = 3

Thus, we have the following table for the points on graph of |x| + 2:

x 0 1 -1
y 2 3 3



The graph of the equation y = |x| + 2:

Question 27

Solution 27




Question 28

Solution 28



Question 29

Solution 29


Question 30

Ravish tells his daughter Aarushi, "Seven years ago, I was seven times as old as you were then. Also, three years form now, I shall be three times as old as you will be". If present ages of Aarushi and Ravish are x and y years respectively, represent this situation algebraically as well as graphically.

Solution 30


Question 31

Solution 31



Chapter 7 - Linear Equations in Two Variables Excercise Ex. 7.4

Question 1

Solution 1


Question 2

Solution 2



y + 3 = 0

y = -3

Point A represents -3 on number line.

On Cartesian plane, equation represents all points on x axis for which y = -3

Question 3

Solution 3



y = 3

Point A represents 3 on number line.

On Cartesian plane, equation represents all points on x axis for which y = 3

Question 4

Solution 4


Question 5

Solution 5


Question 6

Give the geometrical representation of 2x + 13 = 0 as an equation in

One variable

Solution 6



Question 7

Give the geometrical representation of 2x + 13 = 0 as an equation in

Two variables

Solution 7




Question 8

Solve the equation 3x + 2 = x - 8, and represent the solution on (i) the number line.

Solution 8



Question 9

Solve the equation 3x + 2 = x - 8, and represent the solution on (ii) the Cartesian plane.

Solution 9



On Cartesian plane, equation represents all points on y axis for which x = -5

Question 10

Write the equation of the line that is parallel to x-axis and passing through the point

(i) (0,3)

(ii) (0,-4)

(iii) (2,-5)

(iv) (3,4)

Solution 10

(i) The equation of the line that is parallel to x-axis and passing through the point (0,3) is y = 3

(ii) The equation of the line that is parallel to x-axis and passing through the point (0,-4) is y = -4

(iii) The equation of the line that is parallel to x-axis and passing through the point (2,-5) is y = -5

(iv) The equation of the line that is parallel to x-axis and passing through the point (3, 4) is y = 4

Question 11

Solution 11

Chapter 7 - Linear Equations in Two Variables Excercise 7.33

Question 1

If (4, 19) is a solution of the equation y = ax + 3, then a = 

(a) 3

(b) 4

(c) 5

(d) 6

Solution 1

y = ax + 3

If (4, 19) is its solution, then it must satisfy the equation.

Thus, we have

19 = a × 4 + 3

i.e. 4a = 16

i.e. a = 4

Hence, correct option is (b).

Question 2

If (a, 4) lies on the graph of 3x + y = 10, then the value of a is

(a) 3

(b) 1

(c) 2

(d) 4

Solution 2

3x + y = 10

If (a, 4) lies on its graph, then it must satisfy the equation.

Thus, we have

3(a) + 4 = 10

i.e. 3a = 6

i.e. a = 2

Hence, correct option is (c).

Question 3

The graph of the linear equation 2x - y = 4 cuts x-axis at

(a) (2, 0)

(b) (-2, 0)

(c) (0, -4)

(d) (0, 4)

Solution 3

On x-axis, the y-co-ordinate is always 0.

So, 2x - y = 4 will cut the x-axis where y = 0

i.e. 2x = 4

i.e. x = 2

Thus, 2x - y = 4 will cut the x-axis at (2, 0).

Hence, correct option is (a).

Question 4

How many linear equations are satisfied by x = 2 and y = -3?

(a) Only one

(b) Two

(c) Three

(d) Infinitely many

Solution 4

From Point (2, -3) there are infinitely many lines passing in every-direction.

So (2, -3) is satisfied with infinite linear equations.

Hence, correct option is (d).

Question 5

The equation x - 2 = 0 on number line is represented by

(a) a line

(b) a point

(c) infinitely many lines

(d) two lines

Solution 5

Given equation is x – 2 = 0.

If this is treated as an equation in one variable x only, then it has the unique solution x = 2, which is a point on the number line. 

However, when treated as an equation in two variables, it can be expressed as x - 2 = 0.

So as, an equation in two variables, x – 2 = 0 is represented by a single line parallel to y-axis at a distance of 2 units.

Hence, correct option is (a).

Question 6

x = 2, y = -1 is a solution of the linear equation

(a) x + 2y = 0

(b) x + 2y = 4

(c) 2x + y = 0

(d) 2x + y = 5

Solution 6

Substituting x = 2 and y = -1 in the following equations:

L.H.S. = x + 2y = 2 + 2(-1) = 2 - 2 = 0 = R.H.S.

L.H.S. = x + 2y = 2 + 2(-1) = 2 - 2 = 0 ≠ 4 ≠ R.H.S.

L.H.S. = 2x + y = 2(2) + (-1) = 4 - 1 = 3 ≠ 0 ≠ R.H.S.

L.H.S. = 2x + y = 2(2) + (-1) = 4 - 1 = 3 ≠ 5 ≠ R.H.S.

Hence, correct option is (a).

Question 7

If (2k - 1, k) is a solution of the equation 10x - 9y = 12, then k =

(a) 1

(b) 2

(c) 3

(d) 4

Solution 7

If (2k - 1, k) is solution of equation 10x - 9y = 12, then it must satisfy this equation.

Thus, we have

10(2k - 1) - 9k = 12

20k - 10 - 9k = 12

11k = 22

k = 2

Hence, correct option is (b).

Question 8

The distance between the graph of the equations x = -3 and x = 2 is

(a) 1

(b) 2

(c) 3

(d) 5

Solution 8

The distance between the graph of the equations x = -3 and x = 2

= 2 - (-3)

= 2 + 3

= 5

Hence, correct option is (d).

Question 9

The distance between the graphs of the equations y = -1 and y = 3 is

(a) 2

(b) 4

(c) 3

(d) 1

Solution 9

The distance between given two graphs

= 3 - (-1)

= 3 + 1

= 4

Hence, correct option is (b).

Question 10

If the graph of the equation 4x + 3y = 12 cuts the coordinate axes at A and B, then hypotenuse of right triangle AOB is of length

(a) 4 units

(b) 3 units

(c) 5 units

(d) none of these

Solution 10

begin mathsize 12px style 4 straight x space plus space 3 straight y space equals space 12
At space straight x space equals space 0 comma space 3 straight y space equals space 12 rightwards double arrow straight y space equals space 4 space units
At space straight y space equals space 0 comma space 4 straight x space equals space 12 rightwards double arrow straight x space equals space 3 space units
The space triangle space formed space is space triangle AOB comma space where
OB space equals space 4 space units
OA space equals space 3 space units
Hypotenuse space equals space AB space equals space square root of OB squared space plus space OA squared end root space equals space square root of 16 space plus space 9 end root equals 5 space units
Hence comma space correct space option space is space left parenthesis straight c right parenthesis. end style

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