Elimination method
-2x+y=-8
2x+4y=18

We have to add first eq to second eq.
-2x+y+2x+4y=-8+18
5y=10      /:5
y=2
Now we can backsubstitute 
2x+4*2=18
2x+8=18             /-8
2x=18-8
2x=10          /:2
x=5
Finally we obtain result
x=5
y=2

Elimitation method
basically eliminate one of the terms completely
we see that there is a -2x and a 2x in the 2 equations
so just add them together
2x-2x+4y+y=18-8
5y=10
divide both sides by 5
y=2

subsitute
-2x+2=-8
subtract 2 form boht sides
-2x=-10
divide both sides by 2
-x=5
multiply -1
x=5

y=2
x=5