Answer
The solutions of the system are $(-1, 1)$ and $(2,4)$.
Work Step by Step
$y=x +2$
$y=x^2$
Substitute $x +2$ for y
$x +2=x^2$
$x^2-x-2=0$
$(x+1)(x-2)=0$
$x+1=0$ or $x-2=0$
$x=-1$ or $x=2$
Find corresponding y-values. Use either original equation
$y=x+2$
$y=(-1)+2$ or $y=(2)+2$
$y=1$ or $y=4$
The solutions of the system are $(-1, 1)$ and $(2,4)$.