Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 7 - Section 7.2 - Systems of Linear Equations in Three Variables - Concept and Vocabulary Check - Page 829: 3


Equation $2$ does not contain the variable z. To obtain a second equation that does not contain this variable, we can add equations $1$ and $3$.

Work Step by Step

The provided system of equations is as follows; $x+y+z=2$ (I) $2x-3y=3$ (II) $10y-z=12$ (III) It is clear from equation (II) that it does not contain the variable z. In order to get the equation that does not contain z, simply add equations (I) and (III) to get; $\begin{align} & x+y+z+10y-z=2+12 \\ & x+11y=14 \end{align}$ Thus, the above equation contains only the variable x and y but does not contain z.
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