Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 7 - Section 7.1 - Systems of Linear Equations in Two Variables - Concept and Vocabulary Check - Page 817: 7

Answer

$\{(3y+2,y)\}$ (or $\{(x,\frac{1}{3}(x-2))\}$), $dependent$, and $are\ identical$.

Work Step by Step

When we get $10=10$, this means that the system of equations has an infinite set of solutions. From the equation, we have $x=3y+2$ or $y=\frac{1}{3}(x-2)$. Thus the solution set can be expressed as $\{(3y+2,y)\}$ or $(x,\frac{1}{3}(x-2))$. We have a special term for such equations: $dependent$ equations. When graphing such equations, we will end up with lines that $are\ identical$. To summarize, the answers to this question are $\{(3y+2,y)\}$ (or $\{(x,\frac{1}{3}(x-2))\}$), $dependent$, and $are\ identical$.
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