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: 25


$\text{The system is inconsistent.}$

Work Step by Step

The system of equations is given by the following two equations: $$\begin{cases} 2x+y=1 \hspace{20pt} (1)\\[3mm] 4x+2y=3 \hspace{20pt} (2) \end{cases}$$ gives: $\text{Therefore, we add the two equations to eliminate y}$ \[ \begin{aligned} -4x-2y&=-2\\[2mm] 4x+2y&=3 \\[3mm] \hline 0&=1 \\[2mm] \end{aligned} \] $\text{The statement } 0=1 \text{is false, therefore the system is inconsistent.}$
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