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: 15


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: $$\begin{cases} 3x+3y+2z = 4\hspace{20pt} (1)\\[3mm] x-3y+z= 10 \hspace{20pt} (2) \\[3mm] 5x-2y-3z=8 \hspace{20pt} (3) \end{cases}$$ Plugging in $x=2 \text{, } y=-2 \text{ and } z=2$ $$\begin{cases} 3(2)+3(-2)+2(2)=6-6+4 = 4\\[3mm] 2-3(-2)+2 =2+6+2 = 10 \\[3mm] 5(2)-2(-2)-3(2)= 10+4-6 = 8 \end{cases}$$ $\text{Since }x=2 \text{, } y=-2 \text{ and } z=2\text{ satisfy the three equations, then}$ $x=2 \text{, } y=-2 \text{ and } z=2 \text{ are solutions of the system of equations}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.