Question

What is the solution of x+y=2 and 2x+5y=16?

Answer 1

Multiply first equation by -2 an add to second

-2x-2y=-4
2x+5y=16 +
0x+3y=12

3y=12
divide both sides by 3
y=4

sub back
x+y=2
x+4=2
minus 4 both sides
x=-2

x=-2
y=4
(-2,4)

Answer 2

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