Answer
$$y=-2, \quad x=1.$$
Work Step by Step
To get the solution by Gauss elimination, we form the augmented matrix
$$
\left[ \begin {array}{cccc} 1&-2& 5 \\ 3&1&1 \end {array} \right]
.
$$
Multiply the first row by $-3$ and adding it to the second row, we get
$$
\left[ \begin {array}{cccc} 1&-2& 5 \\ 0&7&-14 \end {array} \right]
.
$$
By the back substitution we have
$$y=-2, \quad x=1.$$
