I am trying to solve this system of equations for $s_0$ and $s_1$.
$ s_0 = s_0 (1 - a) + s_1 b \\ s_1 = s_0 a + s_1 (1 - b) $
I have tried to solve each equation one at a time:
$ s_0 = s_0 (1 - a) + s_1 b \\ s_0 - s_0 (1 - a) = s_1 b\\ s_0 a = s_1 b \\ $
$ s_1 = s_0 a + s_1 (1 - b) \\ s_1 - s_1 (1 - b) = s_0 a \\ s_1 b = s_0 a $
Unfortunately, I am only going in circles... eventually, I guessed correctly that $s_0 = \frac{b}{a + b}$ and $s_1 = \frac{a}{a + b}$. How do I actually solve it?