Given the system of equations x − y = 11 and x + y = 9, find the value of 2x - 2y.

Add equation (1) and equation (2):

$$(x - y) + (x + y) = 11 + 9$$ $$2x = 20$$

Divide by 2:

$$x = \frac{20}{2}$$ $$x = 10$$

Substitute $x = 10$ into equation (1):

$$10 - y = 11$$

Subtract 10 from both sides:

$$-y = 11 - 10$$ $$-y = 1$$

Multiply by -1:

$$y = -1$$

Substitute the values $x = 10$ and $y = -1$ into the expression $2x - 2y$:

$$2x - 2y = 2(10) - 2(-1)$$ $$2x - 2y = 20 - (-2)$$ $$2x - 2y = 20 + 2$$ $$2x - 2y = 22$$

Alternatively, notice that $2x - 2y$ can be factored as $2(x - y)$.
From the given equation (1), we know that $x - y = 11$.
Substitute this value directly:

$$2(x - y) = 2(11)$$ $$2(x - y) = 22$$

The value of $2x - 2y$ is $\boxed{22}$.