Answer
$\text{The system is inconsistent.}$
Work Step by Step
The system of equations is given by the following two equations:
$$\begin{cases}
x-y=5 \hspace{20pt} (1)\\[3mm]
-3x+3y=2 \hspace{20pt} (2)
\end{cases}$$
Multiplying equation $ (1)$ by $3$ so that the coefficients of y in the two equations are additive inverses
$3x-3y=15\hspace{20pt} (1)$
$\text{Therefore, we add the two equations to eliminate y}$
\[
\begin{aligned} 3x-3y&=15\\[2mm]
-3x+3y&=2 \\[3mm]
\hline 0&=17 \\[2mm]
\end{aligned}
\]
$\text{The statement } 0=17 \text{ is false, therefore the system is inconsistent.}$
