From the first equation, we can expand the left side:

xy + 10x - y - 10 = 9

Now, we can rearrange the terms by combining like terms:

xy - y + 10x = 19

Next, we can solve the second equation for y:

y = x - 11

Now, substitute y with x - 11 in the rearranged equation:

x(x - 11) - (x - 11) + 10x = 19

Expand and combine like terms:

x^2 - 11x - x + 11 + 10x = 19

Simplify:

x^2 - 2x + 11 = 19

Now, rearrange the terms:

x^2 - 2x - 8 = 0

This is a quadratic equation that can be factored as:

(x - 4)(x + 2) = 0

Solving for x, we get x = 4 or x = -2

Substitute these values back into the equation y = x - 11 to find the corresponding values of y:

For x = 4, y = 4 - 11 = -7
For x = -2, y = -2 - 11 = -13

Therefore, the solutions to the system of equations are x = 4, y = -7 and x = -2, y = -13.