Solving a System of Equations syntax confusion

Question

I have a system of two equations which I would like to solve in terms of a third unknown variable $s$.

PP[s_, x_, y_] := (x + s y) (1 - (x + y)/100) 
QQ[x_]         := x
Solve[{PP == x, QQ == y}, {x, y, s}]

So I should get an equillibrium (x(s),y(s)) after solving the system. I've done this on paper for x = 0 and x>0, but I want to do this on Mathematica. However with my code I get the following error:

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

Any ideas why?

Answer 1

With two equations you can hardly Solve for three variables. If you want x and y to be a function of s don't write s as a variable to be solved:

PP[s_, x_, y_] := (x + s y) (1 - (x + y)/100)
QQ[x_] := x
Solve[{PP[s, x, y] == x, QQ[x] == y}, {x, y}]

(*{{x -> 0, y -> 0}, {x -> (50 s)/(1 + s), y -> (50 s)/(1 + s)}}*)