Find, graphically, the coordinates of the vertices of the triangle formed by the lines:

8y - 3x + 7 = 0, 2x - y + 4 = 0 and 5x + 4y = 29.

Given,

⇒ 8y - 3x + 7 = 0

⇒ 8y = 3x - 7

⇒ y = $\dfrac{3x - 7}{8}$ ………(1)

When x = -3, y = $\dfrac{3 \times -3 - 7}{8} = \dfrac{-9 - 7}{8} = -\dfrac{16}{8}$ = -2,

x = 1, y = $\dfrac{3 \times 1 - 7}{8} = \dfrac{3 - 7}{8} = -\dfrac{4}{8}$ = -0.5

x = 5, y = $\dfrac{3 \times 5 - 7}{8} = \dfrac{15 - 7}{8} = \dfrac{8}{8}$ = 1.

Table of values of equation (1) :

Steps of construction :

1. Plot the points (-3, -2), (1, -0.5), (5, 1) on graph.

2. Join the points.

Given,

⇒ 2x - y + 4 = 0

⇒ y = 2x + 4

When x = -2, y = 2(-2) + 4 = -4 + 4 = 0,

x = -1, y = 2(-1) + 4 = -2 + 4 = 2,

x = 0, y = 2(0) + 4 = 0 + 4 = 4.

Table of values of equation (2) :

Steps of construction :

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

2. Join the points.

Given,

⇒ 5x + 4y = 29

⇒ 4y = 29 - 5x

⇒ y = $\dfrac{29 - 5x}{4}$ ……….(3)

When x = 1, y = $\dfrac{29 - 5 \times 1}{4} = \dfrac{29 - 5}{4} = \dfrac{24}{4}$ = 6,

x = 3, y = $\dfrac{29 - 5 \times 3}{4} = \dfrac{29 - 15}{4} = \dfrac{14}{4}$ = 3.5,

x = 5, y = $\dfrac{29 - 5 \times 5}{4} = \dfrac{29 - 25}{4} = \dfrac{4}{4}$ = 1.

Table of values of equation (3) :

Steps of construction :

1. Plot the points (1, 6), (3, 3.5), (5, 1) on graph.

2. Join the points.

From graph,

These three lines intersect each other at (-3, -2), (5, 1) and (1, 6).

Hence, the coordinates of the vertices of the triangle formed by these lines are (-3, -2), (5, 1) and (1, 6).