# Which ordered pair is the solution to the system of equations y=x and y=x^2-2?

Aug 24, 2016

$\left(x , y\right) = \left(2 , 2\right) \text{ }$ or $\text{ } \left(x , y\right) = \left(- 1 , - 1\right)$

#### Explanation:

If the first equation is satisfied then we can replace $y$ with $x$ in the second equation to get:

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

Subtract $x$ from both sides to get the quadratic:

$0 = {x}^{2} - x - 2 = \left(x - 2\right) \left(x + 1\right)$

Hence solutions $x = 2$ and $x = - 1$.

To make each of these into ordered pair soltuions of the original system, use the first equation again to note that $y = x$.

So the ordered pair solutions to the original system are:

$\left(2 , 2\right) \text{ }$ and $\text{ } \left(- 1 , - 1\right)$