2x+4y=2 2x-2y=-8 using system of elimination

My recommendation is to multiply the equation 2x+4y=2 by -1. That then becomes -2x-4y=-2. Then "add" the two equations together to solve through elimination. The key to elimination is to be able to cancel out one of the variables, as shown below: 
2x-2y=-8
+
-2x-4y=-2
SO: 2x-2x= 0. -2y-4y= -6y and -8-2= -10. The new equation is: -6y=-10 so y= 5/3. Then you plug that in for x and you get (for the first equation) 2x-10/3=-8. -8+10/3= 2x. 2x= -14/3. x=-7/3. 
Plug this back in and check. 
Hope this helps, happy solving! :)