**Question 7. 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.**

Solution:

First equation is x – y + 1 = 0

Add y and subtract 1 both side we get

X = y -1

Plug y = 0 ,1 and 2 we get

X = 0 -1 = - 1

X = 1 -1 = 0

X = 2 -1 = 1

3x + 2y – 12 = 0

Subtract 3x and add 12 both side we get

2y = 12 – 3x

Divide by 2 we get

Y = 6- 1.5 x

Plug x = 0 ,2, and 4 we get

Y = 6- 1.5 *0 = 6

Y = 6- 1.5 *2 = 3

Y = 6- 1.5 *4 = 0

Both lines are intersects at x = 3 and y = 2

**Hence answer is x = 3 and y = 2 **