To solve this system of equations, we can use the method of substitution.
From the second equation, we can solve for x in terms of y:
x - 2y = 11
x = 11 + 2y
Substitute this expression for x into the first equation:
-7x - 2y = -13
-7(11 + 2y) - 2y = -13
-77 - 14y - 2y = -13
-16y = 64
y = -4
Now substitute the value of y back into either of the original equations to solve for x:
x - 2(-4) = 11
x + 8 = 11
x = 11 - 8
x = 3
So the solution to the system of equations is x = 3 and y = -4.
-7x - 2y = -13
x - 2y = 11
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