Question

Which of the following is a solution to the system of nonlinear equations below?

{y=x^2
{y=-x+2

Answer 1

y = x^2 . . . (1)
y = -x + 2 . . . (2)
Putting (1) into (2) gives,
x^2 = -x + 2
x^2 + x - 2 = 0
x^2 - x + 2x - 2 = 0
x(x - 1) + 2(x - 1) = 0
(x + 2)(x - 1) = 0
x = -2 or x = 1
y = (-2)^2 or y = (1)^2
y = 4 or y = 1

Solution is (-2, 4) and (1, 1)