The first equation can be reduced: x+2y=10 so 2y=10-x.
The second equation can be rearranged: 2y=26-3x.
So we have 2y on the left of each so the right hand sides are equal:
26-3x=10-x, 16=2x so x=8 and 2y=10-8=2 so y=1.
The solution is x=8 and y=1 which satisfy both equations.