Getting Composition of a Mixture of Colors
You actually have 3 independent equations.
If one of them is solvable, all three are.  

Now, the equation is given by:

$$ z = \alpha x + \left( 1 - \alpha \right) y $$

Assume $ \alpha, x, z $ are known, then:

$$ y = \frac{z - \alpha x}{1 - \alpha} $$

For any value of $ \alpha \neq 1 $ the solution is valid.
Moreover, if $ alpha = 1 $ then $ z = x $ and $ y $ is irrelevant.  

Looking at the other case, restoring $ x $, yields:

$$ x = \frac{z - \left( 1- \alpha \right) y}{\alpha} $$

For any value of $ \alpha \neq 0 $ the solution is valid.
Moreover, if $ alpha = 0 $ then $ z = y $ and $ x $ is irrelevant.  

As you wrote, in order to have a Linear Interpolation the parameter $ \alpha $ must be in the range $ \left[ 0, 1 \right] $.