I have two equations,
$$\frac{x}{1-x}=\exp(A_{x}+Bx+Cy)$$ $$\frac{y}{1-y}=\exp(A_{y}+Cx+Dy)$$
I am interested in the number of solutions $(x,y)$ to these two equations as the parameters $A_{x},A_{y},B,C,D$ vary. If any help, I know that $B,C,D>0,B+2C+D<1$.
I'd appreciate any and all lead on studying these equations and the number of its solution.
Thank you very much for your help.
Best,
John