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: 10


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

Work Step by Step

The system of equations is given by the following two equations: $$\begin{cases} 2x+\dfrac{1}{2}y=0 \hspace{20pt} (1)\\[3mm] 3x-4y=-\dfrac{19}{2} \hspace{20pt} (2) \end{cases}$$ Plugging in $x=-\dfrac{1}{2} \text{ and } y=2 \text{ in the two equations:}$ $$\begin{cases} 2\left(-\dfrac{1}{2}\right)+\dfrac{1}{2}(2)=-1+1=0 \\[3mm] 3\left(-\dfrac{1}{2}\right)-4(2) = -\dfrac{3}{2}-8=-\dfrac{19}{2} \end{cases}$$ $\text{Since }x=-\dfrac{1}{2} \text{ and } y=2 \text{ satisfy the two equations, then}$ $x=-\dfrac{1}{2} \text{ and } y=2 \text{ are solutions of the system of equations}$
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.