# Linear Equations In Two Variables – Class 9/ Maths.

**Chapter 4 of NCERT/CBSE class 9 Maths is about Linear equations in two variables. Here in this lesson you can find practice problems for this chapter.**

**CBSE CLASS 9 MATHEMATICSLinear Equations In Two Variables – Chapter 4 / Sample Papers.Answer the following questions:**

- If the point (3, 4) lies on the line 2y = ax + 8, then find the value of a?

Solution:

Since the point (3, 4) lies on the line 2y = ax +8, we can write 2 x 4 = a x 3 + 8.

8 = 3a + 8

3a = 8 – 8 = 0

Therefore, a = 0 - Find two solutions for the equation 3x – 2y = 6.

Solution:

Taking x = 0, we get -2y = 6

That is, y = 6/ (-2) = -3.

So (0, -3) is a solution of the given equation.

Similarly, by taking y = 0, we get 3x = 6

That is x = 6/3 = 2.

So (2, 0) is a solution of the given equation. - Show that the points (0, 7), (1, 5), (2, 3) and (4, -1) lie on the graph of the linear equation 2x + y = 7.

Solution:

Given equation is 2x + y = 7

At (0, 7); LHS = 2 x 0 + 7 = 0 + 7 = 7 = RHS.

At (1, 5); LHS = 2 x 1 + 5 = 2 + 5 = 7 = RHS.

At (2, 3); LHS = 2 x 2 + 3 = 4 + 3 = 7 = RHS.

At (4, -1); LHS = 2 x 4 + (-1) = 8 + (-1) = 7 = RHS. - Find the value of k, if x = 3, y = 4 is a solution of the equation 3x – y = k.

Solution:

Given 3x – y = k

Put x = 3 and y = 4 in the given equation 3x – y = k

3 x 3 – 4 = k

9 – 4 = k

5 = k.

So the value of k is 5. - Determine the point on the graph of the linear equation 2x + 3y = 8, whose ordinate is 2 times its abscissa.

Solution:

Given ordinate is 2 times its abscissa, which means that y = 2x.

Put y = 2x in the given equation 2x + 3y = 8, we get 2x + 3(2x) = 8.

2x + 6x = 8

8x = 8

x = 8/8 = 1. - Solve the equation 2x + 1 = x – 3.

Solution:

2x + 1 = x -3

2x – x = -3 -1

x = -4 - Find the co-ordinates of points where the graph of the equation x + 2y = 8 intersects x axis and y axis.

Solution:

Given equation is x + 2y = 8.

For intersection with x axis, y = 0.

Therefore, x = 8.

So the coordinates are (8, 0).

For intersection with y axis, x = 0.

2y = 8

y = 8/2 = 4

So the coordinates are (0, 4).