Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 8 - Section 8.2 - Inconsistent and Dependent Systems and Their Applications - Exercise Set - Page 903: 32

Answer

Solution from Gaussian elimination procedure is $ x=10,y=6\text{ and }z=4$

Work Step by Step

A dependent solution obtained was $\left[ \begin{matrix} k+4 \\ k \\ k-2 \\ \end{matrix} \right]$ And here, $ z $ has a construction limit of 4 cars per min so, $\begin{align} & z=4 \\ & 4=k-2 \\ & \text{ }k=6 \end{align}$ And, $\begin{align} & x=6+4 \\ & y=6 \\ & z=6-2 \end{align}$ So, $ x=10,y=6\text{ and }z=4$ So to keep the traffic moving: 10 cars should be at $ X $, 6 cars at $ Y $ and 4 cars at $ Z $.
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