I have a small problem that delays my project , it seems I am stuck here loads of time. It is probably very easy but I cant see it right now , I am very anxious about this, please take a look:

P0 = (4/5)P0 + (3/4)P1

P1 = (1/5)PO + (1/4)P1

also I know this: P1+P0=1

The solution is P0= 15/19 and P1= 4/19.

I have a very similar problem and I don't know how to continue from this point on, and delays my project!! How am i supposed to solve this ? For more probabilities like P1, P2, P3 what can we do ? Is there some general algorithm for this with steps ?

Thanks a lot people