College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 5 - Section 5.1 - Systems of Linear Equations - 5.1 Exercises - Page 487: 32

Answer

$\text{The system of equations is inconsistent and has no solutions.}$

Work Step by Step

We need to solve the given system of equations: $$3x-2y=5 ~~~(1) \\6x-4y=8 ~~~(2)$$ Multiply first equation by $-2$ and then first equation is equivalent to: $$-6x+4y=-10 ~~~~(3)$$ Add equations $(2)$ and $(3)$ to eliminate $x$. $$6x-4y-6x+4y=8-10 \\ 0=-2 $$ Since $0$ never equals $-2$, the system of equations is inconsistent and has no solutions.
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