Answer
Inconsistent
Work Step by Step
We are given the system of equations:
$\begin{cases}
x-y=5\\
-3x+3y=2
\end{cases}$
Use the elimination method. Multiply the first equation by 3, and add it to the second equation to eliminate $x$ and determine $y$:
$\begin{cases}
3(x-y)=3(5)\\
-3x+3y=2
\end{cases}$
$\begin{cases}
3x-3y=15\\
-3x+3y=2
\end{cases}$
$3x-3y-3x+3y=15+2$
$0=17$
As we got a false statement, the system has no solution. Therefore it is inconsistent.