Solve graphically the simultaneous equations 3y = 5 - x, 2x = y + 3.

Given,

⇒ 3y = 5 - x

⇒ y = $\dfrac{5 - x}{3}$ …….(1)

When x = -4, y = $\dfrac{5 - (-4)}{3} = \dfrac{9}{3}$ = 3,

x = -1, y = $\dfrac{5 - (-1)}{3} = \dfrac{6}{3}$ = 2,

x = 2, y = $\dfrac{5 - 2}{3} = \dfrac{3}{3}$ = 1.

Table of values for equation (1)

Steps of construction :

1. Plot the points (-4, 3), (-1, 2) and (2, 1) on graph paper.

2. Connect points by straight line.

Given,

⇒ 2x = y + 3

⇒ y = 2x - 3 ………..(2)

When x = 0, y = 2 × 0 - 3 = 0 - 3 = -3,

x = 1, y = 2 × 1 - 3 = 2 - 3 = -1,

x = 2, y = 2 × 2 - 3 = 4 - 3 = 1.

Table of values for equation (2)

Steps of construction :

1. Plot the points (0, -3), (1, -1) and (2, 1) on graph paper.

2. Connect points by straight line.

From graph,

The two lines meet at point P(2, 1).

Hence, the solution of the given equations is x = 2, y = 1.