Question

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.

Answer 1

x - y + 1 = 0

x = y - 1

x	0	1	2
y	1	2	3

3x + 2y - 12 = 0

2y = 12 - 3x

y = `(12 - 3y)/2`

x	4	2	0
y	0	3	6

Hence, the graphic representation is as follows:

From the figure, it can be observed that these lines are intersecting each other at point (2, 3) and x-axis at (-1, 0) and (4, 0). Therefore, the vertices of the triangle are (2, 3), (-1, 0), and (4, 0).