Chapter 9 - Quadratic Functions and Equations - 9-8 Systems of Linear and Quadratic Equations - Practice and Problem-Solving Exercises - Page 599: 14

The solutions of the system are $(1, 2)$ and $(-2,5)$.

$y=-x +3$ $y=x^2+1$ 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 $(-2,5)$