Answer
The solutions of the system are $(1, 2)$ and $(-2,5)$.
Work Step by Step
$y=-x +3$
$y=x^2+1$
Substitute $-x +3$ for y
$-x +3=x^2+1$
$x^2+x-2=0$
$(x-1)(x+2)=0$
$x-1=0$ or $x+2=0$
$x=1$ or $x=-2$
Find corresponding y-values. Use either original equation
$y=-x+3$
$y=-(1)+3$ or $y=-(-2)+3$
$y=2$ or $y=5$
The solutions of the system are $(1, 2)$ and $(-2,5)$