I am having trouble with the following simultaneous equations

$\displaystyle x = \alpha x + \beta y $

$\displaystyle y = (1 - \alpha)x + (1 - \beta)y$

$\displaystyle x + y = 1$

I also have the solutions:

$\displaystyle x = \frac{\beta}{1 + \beta - \alpha}$ and $\displaystyle y = \frac{1 - \alpha}{1 + \beta - \alpha}$

but I don't know how these were worked out. Can someone please show me?