# Linear Equations in Two Variables| Worksheet Solutions| Class 9

Worksheet solutions for chapter: Linear Equations in Two Variables for class 9 are provided below.

(1)Express the following linear equations in the form ax + by +c = 0 and indicate the values of a, b and c in each case:

(i) 3x + 5y = 3   (ii) 2x + 4 = 0

Ans-

(i) 3x + 5y = 3 can be written as 3x + 5y – 3 = 0. Here, a = 3, b = 5 and c = -3.

Hence, a = 3, b = 5 and c = -3.

(ii) 2x + 4 = 0

2x + 4 = 0 can be written as 2x + 0.y + 0 = 0.Here, a = -2, b = 3 and c = -6.

Hence, a = 2, b = 0 and c = 0.

(2)Write two solutions for the equation 3x + 6y = 9.

Ans- (3)Find the value of k, if x = 3 and y = 1 is a solution of the equation 6x + y = k.

Ans-

Put x = 3 and y = 1 in equation 6x + y = k

6(3) + 1 = k

18 + 1 = k

19 = k

Or

k = 19

Hence, value of k is 19.

(4)Draw the graph of equation 4x = y.

Ans-

4x = y

4x – y = 0

Solutions of the equation

Put x = 0

4(0) – y = 0

y = 0

Therefore (0, 0) is a solution of given equation.

Put y = 2

4x – 2 = 2

4x = 4

x = 1

Therefore (1, 2) is a solution of given equation.

Hence, (0, 0) and (1, 2) are the two solutions of the given equation.

Solutions of the equations are tabulated below to draw a graph-

 x 0 1 y 0 2 AB is required linear equation in two variables.

(5) Give the equations of two lines passing through (1,7). How many more such lines are there and why?

Ans-

The solutions of equations are (1, 7).

Equations which satisfy these solutions are

x + y = 8

7x = y

These are some equations which can satisfy given solutions. There can be infinite lines or equations which will satisfy the given solutions or coordinates.

(6) If the distance covered by a car is directly proportional to speed of the car. Express this in the form of an equation in two variables and draw a graph by taking constant time as 4 units.

Ans- (7) If the point (2, 6) lies on the graph of the equation x + by = 14, find the value of b.

Ans-

Point (2, 6) lies on the graph of equation x + by = 14.

Therefore, x = 2 and y = 6

Put these values in equation x + by = 14

2 + b (6) = 14

6b = 14 – 2

6b = 12

b = 2

Hence, the value of b is 2.

(8) Write each of the following as an equation in two variables:

(i) x = 5   (ii) 2y = 5

Ans-

(i) x = 5 can be written as x + 0.y -5 = 0.

(ii) 2y = 5 can be written as 0.x + 2y -5 + 0.

(9)A linear equation in two variables has

(i) only one solution

(ii) infinitely many solutions

Ans- (10) The graph of x = a is a straight line parallel to

(i) x – axis

(ii) y- axis

Ans- Helping Topics

Linear equations in two variables

NCERT Solutions, Class 9