A system of equations problem in Mathematica

Question

I have a system of apparently simple equations, but the command below gives an warning message. A little background. Each of the first four equations are based on Bayes' theorem. And it must be the case that $x+y=1$ (probabilities add up to one), and also $x1 + x3 = 1$, $x2 + x4 = 1$, which I have combined into one: $x1+x2+x3+x4=2$. I have added the two last conditions because I have six unknowns. $A1$, $A2$, $A3$, $A4$ are paramaters. But it seems to me something is wrong as below command does not work. Any help is appreciated.

P.S. Warning message:

Solve::svars: Equations may not give solutions for all "solve" variables. 

Thus, it seems I cannot have solutions for $x$, $y$, $x1$, $x2$, $x3$, $x4$ in terms of $A1$, $A2$, $A3$, $A4$.

sol = Solve[{x1 == x A1/(x A1 + y A3), x2 == x A2/(x A2 + y A4), 
   x3 == y A3/(x A1 + y A3), x4 == y A4/(x A2 + y A4), 
   x1 + x2 + x3 + x4 == 2, x + y == 1}, {x1, x2, x3, x4, x, y}]

Answer 1

Your system is underdetermined, because equations $x_1+x_3=1$ and $x_2+x_4=1$ are already implied by the first four equations. That's why Mathematica gives the solution as a function of $y$. You need one more condition to get a single result.