Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 11 - Systems of Equations and Inequalities - Chapter Review - Chapter Test - Page 796: 2


Inconsistent system

Work Step by Step

We are given the system of equations: $\begin{cases} \dfrac{1}{3}x-2y=1\\ 5x-30y=18 \end{cases}$ Multiply the first equation by 3 to clear denominators: $\begin{cases} 3\left(\dfrac{1}{3}x-2y\right)=3(1)\\ 5x-30y=18 \end{cases}$ $\begin{cases} x-6y=3\\ 5x-30y=18 \end{cases}$ Use the elimination method. Multiply the first equation by -5 and add it to the second to eliminate $y$ and find $x$: $-5(x-6y)+5x-30y=-5(3)+18$ $-5x+30y+5x-30y=-15+18$ $0=3$ We got a false statement; therefore the system is inconsistent.
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