Elimination works perfectly here. This method "eliminates" one of the two variables through adding or subtracting the equations.
3x-y=4
+(2x+y=11)
-----------------
5x=15
x=3
Plug in 3 for x into any equation to solve for y.
2(3)+y=11
y=5
answer: x=3, y=5
Merry Christmas!