Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 4 - Review - Page 251: 49

Answer

infinitely many solutions

Work Step by Step

Substituting $x=\dfrac{2}{5}y+2$ into the first equation results to \begin{array}{l}\require{cancel} 5x-2y=10 \\\\ 5\left( \dfrac{2}{5}y+2 \right)-2y=10 \\\\ 2y+10-2y=10 \\\\ 2y-2y=10-10 \\\\ 0=0 \text{ (TRUE)} .\end{array} Since the solution above ended with a TRUE statement, then there are $\text{ infinitely many solutions }$ to the given system of equations.
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