Solve the following simultaneous equations graphically :

x + 3y = 8, 3x = 2 + 2y.

Given,

Equation :

x + 3y = 8

x = 8 - 3y ……….(1)

When, y = 1, x = 8 - 3(1) = 8 - 3 = 5,

y = 2, x = 8 - 3(2) = 8 - 6 = 2,

y = 3, x = 8 - 3(3) = 8 - 9 = -1.

Table of values for equation (1)

Steps of construction :

1. Plot the points (-1, 3), (2, 2) and (5, 1) on graph paper.

2. Connect points by straight line.

Given,

Equation :

⇒ 3x = 2 + 2y

⇒ x = $\dfrac{2 + 2y}{3}$ ……….(2)

When, y = -1, x = $\dfrac{2 + 2 \times -1}{3} = \dfrac{2 - 2}{3}$ = 0.

y = 2, x = $\dfrac{2 + 2 \times 2}{3} = \dfrac{6}{3}$ = 2,

y = 5, x = $\dfrac{2 + 2 \times 5}{3} = \dfrac{12}{3}$ = 4.

Table of values for equation (2)

Steps of construction :

1. Plot the points (0, -1), (2, 2) and (4, 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, 2).

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