Question

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

Answer 1

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

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).