Take 1 cm to represent 1 unit on each axis to draw the graphs of the equations 4x - 5y = -4 and 3x = 2y - 3 on the same graph sheet (same axes). Use your graph to find the solution of the above simultaneous equations.

Given,

Equation :

⇒ 4x - 5y = -4

⇒ 5y = 4x + 4

⇒ y = $\dfrac{4x + 4}{5}$………….(1)

When, x = -1, y = $\dfrac{4 \times -1 + 4}{5} = \dfrac{0}{5}$ = 0,

x = 1.5, y = $\dfrac{4 \times 1.5 + 4}{5} = \dfrac{10}{5}$ = 2,

x = 4, y = $\dfrac{4 \times 4 + 4}{5} =\dfrac{20}{5}$ = 4.

Table of values for equation (1)

Steps of construction :

1. Plot the points (-1, 0), (1.5, 2) and (4, 4) on graph paper.

2. Connect points by straight line.

Given,

Equation :

⇒ 3x = 2y - 3

⇒ 2y = 3x + 3

⇒ y = $\dfrac{3x + 3}{2}$ …………(2)

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

x = 0, $y = \dfrac{3 \times 0 + 3}{2} = \dfrac{3}{2}$ = 1.5,

x = 1, $y = \dfrac{3 \times 1 + 3}{2} = \dfrac{6}{2}$ = 3.

Table of values for equation (2)

Steps of construction :

1. Plot the points (-1, 0), (0, 1.5) and (1, 3) 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(-1, 0).

Hence, the solution of the given equations is x = -1, y = 0.