You can put this solution on YOUR website! Multiply the first equation by -2 and then add the two equations together:
-2(x -2y = 6) yields -2x + 4y = -12
(-2x + 4y = -12) + (2x + y = 4) yields 5y = -8
Solve for y:
5y = -8
y = -8/5
Multiply the second equation by 2 and then add the two equations together:
2(2x + y = 4) yields 4x +2y = 8
(x-2y=6) + (4x+2y=8) yields 5x = 14
Solve for x:
5x = 14
x = 14/5
To check these answers substitute them into the original equations.