Remember in order to use elimination you must have opposite signs so lets make the x in equation one -2 so we can eliminate
-2(x+y=2)
-2x-2y=-4
2x+5y=16
so we get 3y=12 now divide both sides by 3 to get
y=4
so now you must plug y into one of your equations
x+4=2 so now you must get red of the 4 by subtracting four from both sides so that x=-2
so the solution is (-2,4)
Please let me know if you have questions