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 - 11.1 Systems of Linear Equations: Substitution and Elimination - 11.1 Assess Your Understanding - Page 715: 25



Work Step by Step

We are given the system of equations: $\begin{cases} 3x-6y=2\\ 5x+4y=1 \end{cases}$ Use the elimination method. Multiply the first equation by 2, multiply the second equation by 3, and add them to eliminate $y$ and determine $x$: $\begin{cases} 2(3x-6y)=2(2)\\ 3(5x+4y)=3(1) \end{cases}$ $\begin{cases} 6x-12y=4\\ 15x+12y=3 \end{cases}$ $6x-12y+15x+12y=4+3$ $21x=7$ $x=\dfrac{7}{21}$ $x=\dfrac{1}{3}$ Determine $y$ using the first equation: $3x-6y=2$ $3\left(\dfrac{1}{3}\right)-6y=2$ $1-6y=2$ $6y=-1$ $y=-\dfrac{1}{6}$ The solution set of the system is: $\left\{\left(\dfrac{1}{3},-\dfrac{1}{6}\right)\right\}$
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