# What are the solution(s) to the following system of equations y = x^2 and y = –x?

##### 1 Answer
Jul 20, 2016

Since $y = {x}^{2}$ and $y = - x$:

${x}^{2} = - x$

${x}^{2} + x = 0$

$x \left(x + 1\right) = 0$

$x = 0 \mathmr{and} - 1$

$y = {0}^{2} \mathmr{and} {\left(- 1\right)}^{2} = 0 \mathmr{and} 1$

Hence, the solution set is $\left\{0 , 0\right\}$ and $\left\{- 1 , 1\right\}$.

Hopefully this helps!