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

3x – y = 7

2x + 4y = 0

Given 3x – y = 7 … (1)

2x + 4y = 0 … (2)

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

⇒ 3x – y = 7

⇒ 3x - 7 = y … (3)

Substituting (3) in (2),

⇒ 2x + 4y = 0

⇒ 2x + 4 (3x – 7) = 0

⇒ 2x + 12x – 28 = 0

⇒ 14x – 28 = 0

⇒ 14x = 28

∴ x = 2

Substituting x value in (3),

⇒ 3x – 7 = y

⇒ 3 (2) – 7 = y

∴ y = -1

∴ By solving, we get x = 2 and y = -1.

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 3x – y = 7

⇒ y = 3x – 7

For 2x + 4y = 0

⇒ x = -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, -1), hence the solution to this pair is (2, -1).

Hence x and y values satisfy equations (1) and (2).