Answer
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.
