Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 11 - Systems of Equations and Inequalities - Chapter Review - Review Exercises - Page 794: 4



Work Step by Step

We are given the system of equations: $\begin{cases} y=2x-5\\ x=3y+4 \end{cases}$ Use the substitution method. Substitute the expression of $y$ from the first equation into the second to eliminate $y$ and find $x$: $x=3(2x-5)+4$ $x=6x-15+4$ $x=6x-11$ $5x=11$ $x=\dfrac{11}{5}$ Substitute $x=\dfrac{11}{5}$ in the first equation of the given system and determine $y$: $y=2x-5$ $y=2\left(\dfrac{11}{5}\right)-5$ $y=\dfrac{22}{5}-5$ $y=-\dfrac{3}{5}$ The solution set is: $\left\{\left(\dfrac{11}{5},-\dfrac{3}{5}\right)\right\}$
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