step 1
Find the intersection point between the line y=-2.5x+18 and line y=8
so
y=-2.5x+18 -------> equation A
y=8 -----> equation B
substitute equation B in equation A
8=-2.5x+18
solve for x
2.5x=18-8
2.5x=10
x=4
therefore
the first point is (4,8)
step 2
we have the lines
y=-2.5x+18 -------> equation A
y=-x-3 -------> equation C
equate both equations
-2.5x+18=-x-3
solve for x
2.5x-x=18+3
1.5x=21
x=14
Find the value of y
y-x-3
y=-(14)-3
y=-17
therefore
the second point is (14,-17)
step 3
y=8 -----> equation B
y=-x-3 -------> equation C
equate both equations
8=-x-3
x=-3-8
x=-11
therefore
the third point is (-11,8)
step 4
y=1.5x-8 -------> equation D
y=8 -----> equation B
equate both equations
1.5x-8=8
1.5x=16
x=10.67
therefore
the fourth point is (10.67,8)
step 5
y=-2.5x+18 -------> equation A
y=1.5x-8 -------> equation D
equate both equations
2.5x+18=1.5x-8
2.5x-1.5x=-8-18
x=-26
y=1.5(-26)-8
y=-47
therefore
the fifth point is (-26,-47)
step 6
y=-x-3 -------> equation C
y=1.5x-8 -------> equation D
equate both equations
-x-3=-1.5x-8
1.5x-x=-8+3
0.5x=-5
x=-10
y=-(-10)-3
y=7
the point is (-10,7)
the total intersection points are 6
