Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 4 - Section 4.2 - Solving Systems of Linear Equations by Substitution - Practice: 5

Answer

an infinite number of solutions

Work Step by Step

$\begin{cases} -x + 3y = 6 \\ y = \frac{1}{3} x + 2 \end{cases}$ Since we already have a solution for y from the second equation, we just substitute $\frac{1}{3} x + 2$ for y in the first: $-x + 3(\frac{1}{3} x + 2) = 6$ $-x + x + 6 = 6$ $6 = 6$ Since the statement $6 = 6$ is always true, the system has an infinite number of solutions.
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