Answer
The solutions of the system are $(-9,33)$ and $(-12,63)$.
Work Step by Step
$ y=-10x-57$
$y=x^2+11x+51$
Substitute $-10x-57$ for y
$-10x-57=x^2+11x+51$
$x^2+21x+108=0$
$(x+9)(x+12)=0$
$x+9=0$ or $x+12=0$
$x=-9$ or $x=-12$
Find corresponding y-values. Use either original equation:
$ y=-10x-57$
$=-10(-9)-57$ or $ y=-10(-12)-57$
$y=33$ or $y=63$
The solutions of the system are $(-9,33)$ and $(-12,63)$.
