Solve the system by elimination 2x+6y= -12 5x-5y= -10

First thing you should do is reduce coefficients.

1st equation has all multiples of '2'. Divide by 2
---> x +3y = -6

2nd equation has multiples of 5. Divide by 5.
---> x - y = 2

Now elimination part is easier. 
Eliminate 'x' variable by subtracting 2nd equation from 1st.

   x + 3y = -6
-(x  - y = 2)

       4y  = -8

Solve for 'y'
4y = -8

y = (-8)/4 = -2

Substitute value for 'y' back into 2nd equation:
x - (-2) = 2
x + 2 = 2
x = 0

Solution to system is:
x=0, y =-2