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
