# What are the solutions to the following system of equations?y = x^{2} + 3x − 73x − y = −2

What are the solutions to the following system of equations?
$\left\{\begin{array}{l}y={x}^{2}+3x-7\\ 3x-y=-2\end{array}$

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Theodore Schwartz

$\left\{\begin{array}{l}y={x}^{2}+3x-7\\ 3x-y=-2\end{array}$
I'll plug the top into the bottom since it is already y=
$3x-\left({x}^{2}+3x-7\right)=-2$
distribute the negative and get rid of parenthesis
$3x-{x}^{2}-3x+7=-2$
condense $-{x}^{2}+7=-2$
re-write as quadratic with positive ${x}^{2}$
${x}^{2}-9=0$
solve for x
$x=-3$,
$x=3$
plug in each x to get its y
$y=-7$,
$y=11$
solutions: (-3,-7) and (3,11)