[1] 7x + 6y = -10
[2] -2x + y = 11 --> y = 11 + 2x
Replacing [2] in [1]
7x + 6(11 + 2x) = -10
7x + 66 + 12x = -10
7x +12x = -10 -66
19x = -76
x = -76/19
x = -4
Replace x=-4 in [1]
7(-4) + 6y = -10
-28 + 6y = -10
6y = -10 +28
6y = 18
y = 18/6
y = 3
Checking solutions in [2] x=-4, y=3
-2x + y = 11
-2(-4) + 3 = 11
8 + 3 = 11
11 = 11