Chapter 9 - Quadratic Functions and Equations - 9-8 Systems of Linear and Quadratic Equations - Practice and Problem-Solving Exercises - Page 599: 19

The solutions of the system are $(6, -2)$ and $(-9,-47)$.

$y=3x-20$ $y=-x^2+34$ Substitute $3x-20$ for y $3x-20=-x^2+34$ $x^2+3x-54=0$ $(x-6)(x+9)=0$ $x-6=0$ or $x+9=0$ $x=6$ or $x=-9$ Find corresponding y-values. Use either original equation. $y=3x-20$ $y=3(6)-20$ or $y=3(-9)-20$ $y=-2$ or $y=-47$ The solutions of the system are $(6, -2)$ and $(-9,-47)$.