Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 3 Linear Systems and Matrices - 3.4 Solve Systems of Linear Equations in Three Variables - Guided Practice for Examples 1, 2, and 3 - Page 180: 2


No solution

Work Step by Step

We have to solve the system: $$\begin{align*} \begin{cases} x+y-z&=2\quad\quad&&\text{Equation }1\\ 2x+2y-2z&=6\quad\quad&&\text{Equation }2\\ 5x+y-3z&=8\quad\quad&&\text{Equation }3. \end{cases} \end{align*}$$ We multiply equation $1$ by $-2$ and add it to equation $2$: $$\begin{align*} -2x-2y+2z&=-4\quad\quad&&\text{Add }-2\text{ times equation }1\\ 2x+2y-2z&=6\quad\quad&&\text{ }\\ \text{___________}&\text{______}\\ 0&=2\quad\quad&&\text{New Equation }1. \end{align*}$$ As we obtain a false equation, we conclude that the original system has no solution.
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