Algebra 1: Common Core (15th Edition)

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

Chapter 6 - Systems of Equations and Inequalities - 6-1 Solving Systems by Graphing - Practice and Problem-Solving Exercises - Page 369: 43


Answer A

Work Step by Step

Draw a graph to find the solution of the system. $2x+3y=-17$ $\rightarrow 3y=-2x-17$ $\rightarrow y=\frac{-2}{3}x-\frac{17}{3}$ The slope is $\frac{-2}{3}$. The y-intercept is $\frac{17}{3}$. $3x+2y=-8$ $\rightarrow 2y=-3x-8$ $ \rightarrow y=-\frac{3}{2}x-4$ The slope is $-\frac{1}{4}$. The y-intercept is $\frac{5}{4}$. Find the point of intersection. The lines appear to intersect at $(2,-7)$. Check to see if $(2,-7)$ makes both equations true. $y=\frac{-2}{3}x-\frac{17}{3} \rightarrow -7=\frac{-2}{3}(2)-\frac{17}{3} \rightarrow -7=-7$ $y=-\frac{3}{2}x-4 \rightarrow -7=-\frac{3}{2}(2)-4 \rightarrow -7=-7$ The solution of the system is $(2,-7)$. Answer A is correct.
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