`-x+y=4`

`2x-4y=-34`

Write the system of equations as an augmented matrix.

`[[-1,1|4],[2,-4|-34]]`

Multiply the first line by a 2.

`[[-2,2|8],[2,-4|-34]] `

Eliminate the first column.

`[[-2,2|8],[0,-2|-26]]`

`-2y=-26`

`y=13`

`-x+y=4`

`-x+13=4`

`x=9`

The solution set is (9, 13).