Question

What are the solutions to the system: y = x^2 - 2x + 1, y = -2x + 2

Answer 1

Set the two expressions for y equal:
x^2 - 2x + 1 = -2x + 2
x^2 - 2x + 1 + 2x - 2 = 0 → x^2 - 1 = 0 → (x-1)(x+1) = 0

So x = 1 or x = -1. Plugging into y = -2x + 2 gives
x = 1 → y = 0
x = -1 → y = 4

Solutions: (1, 0) and (−1, 4).