## Precalculus (6th Edition) Blitzer

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