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: 36



Work Step by Step

We are given the system of equations: $\begin{cases} \dfrac{1}{2}x+y=-2\\ x-2y=8 \end{cases}$ Use the elimination method. Multiply the first equation by $2$ and add it to the second equation to eliminate $y$ and determine $x$: $\begin{cases} 2\left(\dfrac{1}{2}x+y\right)=2(-2)\\ x-2y=8 \end{cases}$ $\begin{cases} x+2y=-4\\ x-2y=8 \end{cases}$ $x+2y+x-2y=-4+8$ $2x=4$ $x=2$ Determine $y$ using the first equation: $\dfrac{1}{2}x+y=-2$ $\dfrac{1}{2}(2)+y=-2$ $1+y=-2$ $y=-3$ The solution set of the system is: $\left\{\left(2,-3\right)\right\}$
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