Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 2 - Systems of Linear Equations and Inequalities - 2.1 Systems of Linear Equations - 2.1 Exercises - Page 142: 38

Answer

The equations represent one and the same line. The system is dependent. There are infinitely many solutions.

Work Step by Step

The slope of each line is $m=\displaystyle \frac{1}{4}$ and the y-intercepts are the same, $b=4$. The equations represent one and the same line. There are infinitely many points satisfying both equations. So solutions exist. Then, the system is consistent. In this case (infinitely many solutions), we say the system is dependent.
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