## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson

# Chapter 10 - Systems of Equations and Inequalities - Section 10.1 Systems of Linear Equations: Substitution and Elimination - 10.1 Assess Your Understanding - Page 734: 11

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

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