Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 10 - Systems of Equations and Inequalities - Section 10.1 Systems of Linear Equations: Substitution and Elimination - 10.1 Assess Your Understanding - Page 734: 14


The given values of the variables are solutions of the system of equations. $\text{See the work below.}$

Work Step by Step

The system of equations is given by the following three equations: $$\begin{cases} 4x-z=7\hspace{20pt} (1)\\[3mm] 8x+5y-z=0 \hspace{20pt} (2) \\[3mm] -x-y+5z=6 \hspace{20pt} (3) \end{cases}$$ Plugging in $x=2 \text{, } y=-3 \text{ and } z=1$ $$\begin{cases} 4(2)-1 = 8-1 = 7 \\[3mm] 8(2)+5(-3)-1 = 16-15-1= 0 \\[3mm] -2-(-3)+5(1)=-2+3+5= 6 \end{cases}$$ $\text{Since }x=2 \text{, } y=-3 \text{ and } z=1\text{ satisfy the three equations, then }$ $x=2 \text{, } y=-3 \text{ and } z=1 \text{ are solutions of the system of equations.}$
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