Solve the following equations graphically :

3x - 2y = 4, 5x - 2y = 0.

Given,

Equation :

⇒ 3x - 2y = 4

⇒ 2y = 3x - 4

⇒ y = $\dfrac{3}{2}$x - 2 ………(1)

When, x = -2, y = $\dfrac{3}{2} \times -2 - 2$ = -3 - 2 = -5,

x = 0, y = $\dfrac{3}{2} \times 0 - 2$ = 0 - 2 = -2,

x = 2, y = $\dfrac{3}{2} \times 2 - 2$ = 3 - 2 = 1.

Tables of values for equation (1)

Steps of construction :

1. Plot the points (-2, -5), (0, -2) and (2, 1) on graph paper.

2. Connect points by straight line.

Given,

Equation :

⇒ 5x - 2y = 0

⇒ 2y = 5x

⇒ y = $\dfrac{5}{2}x$ …………..(2)

When, x = -2, y = $\dfrac{5}{2} \times -2$ = -5,

x = 0, y = $\dfrac{5}{2} \times 0$ = 0,

x = 2, y = $\dfrac{5}{2} \times 2$ = 5.

Tables of values for equation (2)

Steps of construction :

1. Plot the points (-2, -5), (0, 0) and (2, 5) on graph paper.

2. Connect points by straight line.

The graphs of both the straight lines are shown in the figure.

The lines intersect at point A(-2, -5).

Hence, the solution of the given equations is x = -2, y = -5.