Answer
The student misplaced the values of $x$ and $y$.
Work Step by Step
The given augmented matrix is
$\Rightarrow \left[\begin{array}{cc|c}
0 & 1 & 5\\
1 & 0 & 3
\end{array}\right]$
The first column represents $x$ values, and the second column represents $y$ values.
The solution set is $(x,y)=(3,5)$.