Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 9 - Quadratic Functions and Equations - 9-8 Systems of Linear and Quadratic Equations - Practice and Problem-Solving Exercises - Page 599: 20


The solutions of the system are $(-10, 130)$ and $(-7,100)$.

Work Step by Step

$y+10x=30 \rightarrow y=30-10x$ $y=x^2+7x+100$ Substitute $30-10x$ for y $30-10x=x^2+7x+100$ $x^2+17x+70=0$ $(x+10)(x+7)=0$ $x+10=0$ or $x+7=0$ $x=-10$ or $x=-7$ Find corresponding y-values. Use either original equation $y=30-10x$ $y=30-10(-10)$ or $y=30-10(-7)$ $y=130$ or $y=100$ The solutions of the system are $(-10, 130)$ and $(-7,100)$.
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