Class 9 NCERT Solutions Maths Chapter 4  Linear Equations in Two Variables
Complete your Maths practice with the help of NCERT Solutions for CBSE Class 9 Mathematics Chapter 4 Linear Equations in Two Variables. TopperLearning’s Maths experts show you the steps to solve realworld problems based on linear equations in two variables. In this chapter, you can revise important concepts to enhance your ability to represent linear equations graphically and algebraically.
Linear equations may be tricky, but you can easily learn about them by watching our CBSE Class 9 Maths video lessons. Also, learn to easily plot graphs of linear equations in two variables with our textbook solutions and other resources for this Maths chapter.
Linear Equations in Two Variables Exercise Ex. 4.1
Solution 1
x = 2y
x  2 y = 0
Solution 2
 2x + 3 y  6 = 0
a =  2, b = 3, c =  6
1x  3y + 0 = 0
Comparing this equation with ax + by + c = 0
a = 1, b =  3, c = 0
2x + 5y + 0 = 0
a = 2, b = 5, c = 0
3x + 0.y + 2 = 0
a = 3, b = 0, c = 2
0.x + 1.y  2 = 0
a = 0, b = 1, c =  2
 2x + 0.y + 5 = 0
Company this equation with ax + by + c = 0
a =  2, b = 0, c = 5
Linear Equations in Two Variables Exercise Ex. 4.2
Solution 1
Hence, the correct answer is (iii).
Solution 2
For x = 0
2(0) + y = 7
For x = 1
2(1) + y = 7
2(2) + y = 7
y = 3
For x = 1
(1) + y =9
For x = 0
0 = 4y
For y = 1
x = 4(1) = 4
So, (4, 1) is a solution of this equation
For y =  1
x = 4(1)
x = 4
So, (4,  1) is a solution of this equation
For x = 2
2 = 4y
Solution 3
Putting x = 0, and y = 2 in the L.H.S of given equation
x  2y = 0  (22 )
L.H.S # R.H.S
So (0, 2) is not a solution of this equation.
x  2y = 2  (2 0)
L.H.S R.H.S
So (2, 0) is not a solution of this equation.
Putting x = 4, and y = 0 in the L.H.S of given equation
x  2y = 4  2(0)
= 4 = R.H.S
So (4, 0) is a solution of this equation.
L.H.S R.H.S
So is not a solution of this equation.
Putting x = 1, and y = 1 in the L.H.S of given equation
x  2y = 1  2(1)
L.H.S R.H.S
So (1, 1) is not a solution of this equation.
Solution 4
2(2) + 3(1) = k
4 + 3 = k
k = 7
Linear Equations in Two Variables Exercise Ex. 4.3
Solution 1
x 
0 
4 
y 
4 
0 
x 
4 
2 
y 
2 
0 
Now we can draw the graph of above equation as following
We may observe that x =  1, y =  3 and x = 1, y = 3 are solutions of above equation. So our solution table is
x 
 1 
1 
y 
 3 
3 
Now we may draw the graph of above equation as following
x 
0 
1 
y 
3 
1 
Now we may construct the graph of this equation as below
Solution 2
2x + y 18 = 0.
As we know that through one point, infinite number of lines can pass through.
So, there are infinite lines of such type passing through given point.
Solution 3
3y = ax + 7
3 (4) = a (3) + 7
5 = 3a
a =
Solution 4
Fair for 1st kilometre = Rs .8
Fair for rest distance = (x  1) 5
Total fair = 8 + (x  1) 5
y = 8 + 5x  5
y = 5x + 3
5x  y + 3 = 0
x 
0 

y 
3 
0 
Solution 5
We may observe that coordinates of the points of the graph satisfy the equation x + y = 0.
So, x + y = 0 is the equation corresponding to graph as shown in the first figure.
Hence (ii) is the correct answer.
So y =  x + 2 is the equation corresponding to the graph shown in the second figure.
Hence,
Solution 6
Work done distance traveled
w d
w = kd
Where k is a constant
If constant force is 5 units, work done w = 5d
Now we may observe that point (1, 5) and (1, 5) satisfy the above equation.
So (1, 5) and (1, 5) are solutions of this equation.
The graph can be drawn as follows:
(ii) From the graphs we may observe that the value of y corresponding to x = 0 is 0. Thus the work done by the body is 0 units when the distance traveled by it is 0 unit.
Solution 7
Amount contributed by Yamini + amount contributed by Fatima = 100
x + y = 100
Now we observe that (100, 0) and (0, 100) satisfy the above equation.
So, (100, 0) and (0, 100) are solutions of above equation.
The graph of equation x + y = 100 can be drawn as follows:
Solution 8
Now we can draw the graph of above equation as below
If F = 0^{o}
Linear Equations in Two Variables Exercise Ex. 4.4
Solution 1
In two variables y = 3 represents a straight line passing through point (0, 3) and parallel to x axis. As it is a collection of all points of plane which are having their y coordinate as 3
Solution 2
(2) In two variables 2x + 9 = 0 represents a straight line passing through point ( 4.5, 0) and parallel to y axis. As it is a collection of all points of plane, having their x coordinate as 4.5.