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: 2

Answer

$\left\{\left(2,\dfrac{1}{2}\right)\right\}$

Work Step by Step

We are given the system of equations: $\begin{cases} 3x-4y=4\\ x-3y=\dfrac{1}{2} \end{cases}$ Use the elimination method. Multiply the second equation by -3 and add it to the first to eliminate $x$ and find $y$: $3x-4y-3(x-3y)=4-3\left(\dfrac{1}{2}\right)$ $3x-4y-3x+9y=4-\dfrac{3}{2}$ $5y=\dfrac{5}{2}$ $y=\dfrac{1}{2}$ Substitute $y=\dfrac{1}{2}$ in the first equation of the given system and determine $x$: $3x-4y=4$ $3x-4\left(\dfrac{1}{2}\right)=4$ $3x-2=4$ $3x=6$ $x=2$ The solution set is: $\left\{\left(2,\dfrac{1}{2}\right)\right\}$
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