## 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.

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

 X -1 0 1 Y 0 1 2

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

 X 0 2 4 Y 6 3 0

Both lines are intersects at x = 3 and y = 2
Hence answer is x = 3 and y = 2

Question 7. Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determin