8x + 11y = -50 [1]
-32x + 44y = -200 [2]
For the elimination method you want to be able to add the equations so that one of the letters (i.e. 'x' or 'y') disappears.
So first you can divide both sides of equation [2] by 4:
This will give, -32x/4 + 44y/4 = -200/4
-8x + 11y = -50
So now when you add both equations together:
8x + 11y = -50
+ -8x + 11y = -50
22y = -100
y = -50/11
Now you can simply substitute this value into one of the original equations to find x:
8x + 11y = -50 [1]
8x + 11 x (-50/11) = -50
8x - 50 = -50
8x -50 + 50 = -50 + 50
8x = 0
x = 0
So the final solutions are y = -50/11 and x = 0