Let us solve the following equations in two variables by the method of substitution and check them graphically.

Given … (1)

And … (2)

Expressing x of equation (1) in terms of y,

… (3)

Substituting (3) in (2),

⇒ 12 + 4y = 2 (12)

⇒ 12 + 4y = 24

⇒ 4y = 24 – 12

∴ y = 3

Substituting y value in (3),

∴ x = 2

∴ By solving, we get x = 2 and y = 3.

Justification:

Generally, we substitute x = 0 or y = 0 in the given linear equations to get y and x. So we get two points on the straight line. To find more points on the line, take different values of x related to it, we get different values for y from the equation.

We get the following tables for the given linear equations.

For

For

∴ x = 8 – 2y

Plotting these points on a graph and joining them, we get two straight lines.

From the graph, we can see that both lines intersect at (2, 3), hence the solution to this pair is (2, 3).

Hence we can say that x and y values satisfy equations (1) and (2).