Answer
The solutions of the system are $(10,145)$ and $(6,69)$.
Work Step by Step
$y+45=19x \rightarrow y=19x-45$
$y=x^2+3x+15$
Substitute $19x-45$ for y
$19x-45=x^2+3x+15$
$x^2-16x=60=0$
$(x-10)(x+13)=0$
$x-10=0$ or $x-6=0$
$x=10$ or $x=6$
Find corresponding y-values. Use either original equation
$ y=19x-45$
$=19(10)-45$ or $ y=19(6)-45$
$y=145$ or $y=69$
The solutions of the system are $(10,145)$ and $(6,69)$
