Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 3 - Section 3.1 - Systems of Linear Equations in Two Variables - 3.1 Exercises - Page 228: 65

Answer

The equations have the same slopes, and the same y-intercepts. Therefore, the equations are dependent, there is infinite solutions.

Work Step by Step

First equation: $2x=-3y+1$ $3y=-2x+1$ $y=-\frac{2}{3}x+\frac{1}{3}$ Second equation: $6x=-9y+3$ $9y=-6x+3$ $y=-\frac{6}{9}x+\frac{3}{9}=-\frac{2}{3}x+\frac{1}{3}$ This means that the equations have the same slopes, and the same y-intercepts. Therefore, the equations are dependent, there is infinite solutions.
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