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: 38



Work Step by Step

We are given the system of equations: $\begin{cases} \dfrac{1}{3}x-\dfrac{3}{2}y=-5\\ \dfrac{3}{4}x+\dfrac{1}{3}y=11 \end{cases}$ Multiply the first equation by 6 and the second equation by 12 to eliminate denominators: $\begin{cases} 6\left(\dfrac{1}{3}x-\dfrac{3}{2}y\right)=6(-5)\\ 12\left(\dfrac{3}{4}x+\dfrac{1}{3}y\right)=12(11) \end{cases}$ $\begin{cases} 2x-9y=-30\\ 9x+4y=132 \end{cases}$ Use the elimination method. Multiply the first equation by $-9$, multiply the second equation by 2, and add them to eliminate $x$ and determine $y$: $\begin{cases} -9(2x-9y)=-9(-30)\\ 2(9x+4y)=2(132) \end{cases}$ $\begin{cases} -18x+81y=270\\ 18x+8y=264 \end{cases}$ $-18x+81y+18x+8y=270+264$ $89y=534$ $y=\dfrac{534}{89}$ $y=6$ Determine $x$ using the first equation: $2x-9y=-30$ $2x-9(6)=-30$ $2x-54=-30$ $2x=-30+54$ $2x=24$ $x=12$ The solution set of the system is: $\left\{\left(12,6\right)\right\}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.