Answer
The solutions of the system are $(9, -71)$ and $(-11,-91)$.
Work Step by Step
$x=y+80 \rightarrow y=x-80$
$y=-x^2-x+19$
Substitute $x-80$ for y
$x-80=-x^2-x+19$
$x^2+2x-99=0$
$(x-9)(x+11)=0$
$x-9=0$ or $x+11=0$
$x=9$ or $x=-11$
Find corresponding y-values. Use either original equation
$y=x-80$
$y=9-80$ or $y=(-11)-80$
$y=-71$ or $y=-91$
The solutions of the system are $(9, -71)$ and $(-11,-91)$.
