Answer
The solutions of the system are $(4,5)$ and $(-12,85)$.
Work Step by Step
$ y=25-5x$
$y=x^2+3x-23$
Substitute $25-5x$ for y
$25-5x=x^2+3x-23$
$x^2+8x-48=0$
$(x-4)(x+12)=0$
$x-4=0$ or $x+12=0$
$x=4$ or $x=-12$
Find corresponding y-values. Use either original equation:
$ y=25-5x$
$y=25-5(4)$ or $ y=25-5(-12)$
$y=5$ or $y=85$
The solutions of the system are $(4,5)$ and $(-12,85)$.
