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: 20


$x=-1, y =2 \text{ or } (-1, 2)$

Work Step by Step

The system of equations is given by the following two equations: $$\begin{cases} x+3y=5 \hspace{20pt} (1)\\[3mm] 2x-3y=-8 \hspace{20pt} (2) \end{cases}$$ $\text{The coefficients of y in the two equations are additive inverses.}$ $\text{Therefore, we add the two equations to eliminate y"}$ \[ \begin{aligned} &x+3y=5 \\[2mm] &2x-3y=-8 \\[3mm] \hline & 3x=-3 \\[2mm] &x =-1 \end{aligned} \] $\text{Substituting in equation (1) for } x=-1$ gives: $$-1+3y=5\\[3mm]3y=5+1 \\[3mm] 3y=6 \\[3mm] y=2$$ Therefore, the solution is: $\boxed{x=-1 \hspace{20pt} y =2}$
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