## Precalculus (10th Edition)

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.