Question

How many solutions does the system have?

y = –2x + 2
y = x2 – 3x

Answer 1

for you problem is the equations?

y=-2x+2
&
y=2x-3x

then it would be one solution because they are two straight lines that don't have the same slope.

Answer 2

y = -2x + 2
y = x² - 3x

-2x + 2 = x² - 3x
+ 2x + 2x
2 = x² - x
2 - 2 = x² - x - 2
0 = x² - x - 2
x = -(-1) ± √((-1)² - 4(1)(-2))
2(1)
x = 1 ± √(1 + 8)
2
x = 1 ± √(9)
2
x = 1 ± 3
2
x = 1 + 3 or x = 1 - 3
2 2
x = 4 or x = -2
2 2
x = 2 or x = -1

y = -2x + 2
y = -2(2) + 2 or y = -2(-1) + 2
y = -4 + 2 or y = 2 + 2
y = -2 or y = 4
(x, y) = (2, -2) or (-1, 4)

The system has two solutions, which is equal to (2, -2) and (-1, 4).