Answer
The solutions of the system are $(-8,3)$ and $(12,123)$.
Work Step by Step
$y=6x+51$
$y=x^2+2x-45$
Substitute $6x+51$ for y
$6x+51=x^2+2x-45$
$x^2-4x-96=0$
$(x-12)(x+8)=0$
$x+8=0$ or $x-12=0$
$x=-8$ or $x=12$
Find corresponding y-values. Use either original equation $y=6x+51$
$y=6(-8)+51$ or $y=6(12)+51$
$y=3$ or $y=123$
The solutions of the system are $(-8,3)$ and $(12,123)$.
