Question

What are the ordered pairs of the solutions for this system of equations? y = -x2 + 2 y = x​

Answer 1

Answer:

The solutions of this system of equations are (-2, -2) and (1, 1).

Step-by-step explanation:

Let be the following system of equations:

$y = -x^{2}+2$ (1)

$y = x$ (2)

(2) in (1):

$y = -y^{2}+2$

$y^{2}+y-2 = 0$

This polynomial can be solved analytically by Quadratic Formula:

$y_{1} = 1$, $y_{2} = -2$

Hence, the solutions of this system of equations are (-2, -2) and (1, 1).