Solve the following system of equations graphically :

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

Given,

⇒ x - 2y - 4 = 0

⇒ 2y = x - 4

⇒ y = $\dfrac{x - 4}{2}$ ………(1)

When x = -2, y = $\dfrac{-2 - 4}{2} = -\dfrac{6}{2}$ = -3,

x = 0, y = $\dfrac{0 - 4}{2} = -\dfrac{4}{2} = -2$,

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

Table of values of equation (1) :

Steps of construction :

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

2. Join the points.

Given,

⇒ 2x + y - 3 = 0

⇒ y = 3 - 2x ………(2)

When x = 0, y = 3 - 2(0) = 3 - 0 = 3,

x = 1, y = 3 - 2(1) = 3 - 2 = 1,

x = 2, y = 3 - 2(2) = 3 - 4 = -1.

Table of values of equation (2) :

Steps of construction :

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

2. Join the points.

From graph,

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

Hence, x = 2, y = -1.