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: 9

Answer

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: $$\begin{cases} 3x-4y=4 \hspace{20pt} (1)\\[3mm] \dfrac{1}{2}x-3y=-\dfrac{1}{2} \hspace{20pt} (2) \end{cases}$$ Plugging in $x=2 \text{ and } y=\dfrac{1}{2} \text{ in the two equations:}$ $$\begin{cases} 3(2)-4 \left(\dfrac{1}{2} \right)=6 -2= 4 \\[3mm] \dfrac{1}{2}(2)-3\left(\dfrac{1}{2} \right) = 1-\dfrac{3}{2}= - \dfrac{1}{2} \end{cases}$$ $\text{Since }x=2 \text{ and } y=\dfrac{1}{2} \text{ satisfy the two equations, then}$ $x=2 \text{ and } y=\dfrac{1}{2} \text{ are solutions of the system of equations}$
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