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: 17


$x=6, y =2 \text{ or }(6, 2)$

Work Step by Step

The system of equations is given by the following two equations: $$\begin{cases} x+y=8 \hspace{20pt} (1)\\[3mm] x-y=4 \hspace{20pt} (2) \end{cases}$$ $\text{The coefficients of y in the two equations are additive inverses.}$ $\text{Therefore, we add the two equations to eliminate y}$ \[ \begin{aligned} &x+y =8\\[2mm] &x-y=4 \\[3mm] \hline & 2x=12 \\[2mm] &x =6 \end{aligned} \] $\text{Substituting in equation (1) for } x=6$ $$6+y=8 \\[3mm]y=8-6 \\[3mm] y = 2$$ Therefore, the solution is: $\boxed{x=6 \hspace{20pt} y =2 \hspace{20pt} \text{ or }\hspace{20pt} (6, 2)}$
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