Use graph paper for this question :

(i) Draw the graphs of 3x - y - 2 = 0 and 2x + y - 8 = 0. Take 1 cm = 1 unit on both axes and plot three points per line.

(ii) Write down the coordinates of the point of intersection and the area of the triangle formed by the lines and the x-axis.

(i) Given,

⇒ 3x - y - 2 = 0

⇒ y = 3x - 2 …………(1)

When x = 0, y = 3 × 0 - 2 = 0 - 2 = -2,

x = 1, y = 3 × 1 - 2 = 3 - 2 = 1,

x = 2, y = 3 × 2 - 2 = 6 - 2 = 4.

Table of values for equation (1)

Steps of construction :

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

2. Join the points.

Given,

⇒ 2x + y - 8 = 0

⇒ y = 8 - 2x ………..(2)

When x = 2, y = 8 - 2 × 2 = 8 - 4 = 4,

x = 3, y = 8 - 2 × 3 = 8 - 6 = 2,

x = 4, y = 8 - 2 × 4 = 8 - 8 = 0.

Table of values for equation (2)

Steps of construction :

1. Plot the points (2, 4), (3, 2) and (4, 0).

2. Join the points.

(ii) From the graph,

P(2, 4) is the point of intersection of lines.

BC = $3\dfrac{2}{3}$ cm

PV = 4 cm.

Area of triangle = $\dfrac{1}{2}$ × base × height

= $\dfrac{1}{2}$ × BC × PV

= $\dfrac{1}{2} \times 3\dfrac{2}{3}$ × 4

= $6\dfrac{2}{3}$ cm².

Hence, P(2, 4) is the point of intersection of lines and area = $6\dfrac{2}{3}$ cm².