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 716: 48



Work Step by Step

We are given the system of equations: $\begin{cases} 2x-3y-z=0\\ -x+2y+z=5\\ 3x-4y-z=1 \end{cases}$ Use the elimination method. Add the second equation to the first, and then add it to the third equation: $\begin{cases} 2x-3y-z-x+2y+z=0+5\\ 3x-4y-z-x+2y+z=1+5 \end{cases}$ $\begin{cases} x-y=5\\ 2x-2y=6 \end{cases}$ $\begin{cases} x-y=5\\ x-y=3 \end{cases}$ Multiply the first equation by -1, and add it to the second equation to eliminate $y$ and determine $x$: $\begin{cases} -x+y=-5\\ x-y=3 \end{cases}$ $-x+y+x-y=-5+3$ $0=-2$ As we got a false statement, the system has no solution; it is inconsistent.
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