Question

Help please. Thanks in advance

Answer 1

Since they want only the coordinates of the vertices. You only care about where the lines intersect, the greater than, less than signs are irrelevant.

Get each equation in 'y=mx+b' form
1)  y = -x + 9
2)  y = 2x-21
3)  y = -4x +15

Now you can set any 2 equations equal to each other and solve for 'x'.
This will be the 'x' coordinate of the point where the 2 lines intersect.
You need 3 points, so you will need 3 different sets of 2 equations:

1) = 2)
2x -21 = -x+9
3x = 30
x = 10  -----> y = -(10)+9 = -1


1) = 3)
-x+9 = -4x+15
3x = 6
x = 2  -------> y = -(2) + 9 = 7

2) = 3)
2x - 21 = -4x+15
6x = 36
x = 6  ---------> y = 2(6) -21 = -9

Therefore the 3 intersecting points are:
(10,-1)
(2, 7)
(6, -9)