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).