Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 6 - Systems of Equations and Inequalities - 6-1 Solving Systems by Graphing - Practice and Problem-Solving Exercises - Page 368: 38


The system has only one solution.

Work Step by Step

We are given $3x+2y=1 $ $\rightarrow 2y=-3x+1$ $ \rightarrow y=\frac{-3}{2}x+\frac{1}{2}$ The slope is $\frac{-3}{2}$. $4y=6x+2$ $ \rightarrow y=\frac{3}{2}x+\frac{1}{2}$ The slope is $\frac{3}{2}$. The lines intersect at one point. The lines have different slopes. The equations are consistent and independent. Therefore, the system has only one solution.
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