Solve the following simultaneous equations, graphically :

2x - 3y + 2 = 4x + 1 = 3x - y + 2.

Considering,

⇒ 2x - 3y + 2 = 4x + 1

⇒ 3y = 2x - 4x + 2 - 1

⇒ 3y = -2x + 1

⇒ y = $\dfrac{1 - 2x}{3}$ ………(1)

When, x = -4, y = $\dfrac{1 - 2 \times (-4)}{3} = \dfrac{1 + 8}{3} = \dfrac{9}{3}$ = 3,

x = -1, y = $\dfrac{1 - 2 \times (-1)}{3} = \dfrac{1 + 2}{3} = \dfrac{3}{3}$ = 1,

x = 2, y = $\dfrac{1 - 2 \times 2}{3} = \dfrac{1 - 4}{3} = \dfrac{-3}{3}$ = -1.

Table of values for equation (1)

Steps of construction :

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

2. Connect points by straight line.

Considering,

⇒ 4x + 1 = 3x - y + 2

⇒ y = 3x - 4x + 2 - 1

⇒ y = -x + 1

⇒ y = 1 - x …………(2)

When, x = 0, y = 1 - 0 = 1,

x = 1, y = 1 - 1 = 0,

x = 2, y = 1 - 2 = -1.

Table of values for equation (2)

Steps of construction :

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

2. Connect points by straight line.

From graph,

The two lines intersect at P(2, -1).

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