How many solutions does the system have?

y = - 2x + 2

y = x2 - 3x

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.

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).