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: 22


$x= -\dfrac{23}{4}, y =4 \text{ or } \left(-\dfrac{23}{4}, 4\right)$

Work Step by Step

The system of equations is given by the following two equations: $$\begin{cases} 4x+5y=-3 \hspace{20pt} (1)\\[3mm] -2y=-8 \hspace{20pt} (2) \end{cases}$$ $\text{Solving equation (2) for y}$ gives: $$-2y=-8 \\[3mm] 2y=8 \\[3mm] y = 4$$ $\text{Substituting in equation (1) for } y=4$ gives: $$4x+5(4)=-3 \\[3mm] 4x+20= -3 \\[3mm] 4x=-23 \\[3mm] x= -\dfrac{23}{4}$$ Therefore, the solution is: $\boxed{x= -\dfrac{23}{4} \hspace{20pt} y =4}$
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