Draw the graphs of the equations x - y + 1 = 0 and 3x + 2y - 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

Given,

1st equation : x - y + 1 = 0

⇒ y = x + 1 ………(1)

2nd equation : 3x + 2y - 12 = 0

⇒ 2y = 12 - 3x

⇒ y = $\dfrac{12 - 3x}{2}$ ………(2)

Table for equation (1),

Table for equation (2),

Steps of construction :

1. Plot the points (0, 1) and (4, 5) join them to form equation (1).

2. Plot the points (0, 6) and (2, 3) and join them to form equation (2).

3. The lines intersect at K(2, 3).

From graph,

x - y + 1 = 0 meets x-axis at point (-1, 0) and 3x + 2y - 12 = 0 meets x-axis at point (4, 0).

Hence, coordinates of vertices of triangle are (2, 3), (-1, 0) and (4, 0).