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: 31


$\{(x,y)|x=4-2y,y\text{ is any real number}\}$

Work Step by Step

We are given the system of equations: $\begin{cases} x+2y=4\\ 2x+4y=8 \end{cases}$ Use the elimination method. Multiply the first equation by $-2$ and add it to the second equation to eliminate $y$ and determine $x$: $\begin{cases} -2(x+2y)=-2(4)\\ 2x+4y=8 \end{cases}$ $\begin{cases} -2x-4y=-8\\ 2x+4y=8 \end{cases}$ $-2x-4y+2x+4y=-8+8$ $0=0$ As we got an identity, the system has infinitely many solutions. We solve the first equation in terms of $y$: $x=4-2y$ The solution set of the system is: $\{(x,y)|x=4-2y,y\text{ is any real number}\}$
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