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: 27



Work Step by Step

We are given the system of equations: $\begin{cases} 2x+y=1\\ 4x+2y=3 \end{cases}$ Use the elimination method. Multiply the first equation by -2, and add it to the second equation to eliminate $x$ and determine $y$: $\begin{cases} -2(2x+y)=-2(1)\\ 4x+2y=3 \end{cases}$ $\begin{cases} -4x-2y=-2\\ 4x+2y=3 \end{cases}$ $-4x-2y+4x+2y=-2+3$ $0=1$ As we got a false statement, the system has no solution. Therefore it is inconsistent.
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