Question: Solving a system with 13 equations not possible

Dear reader,

For a concept evaluation I need a system of 13 equations to be solved. Not necesserarily explicitliy, it would be sufficient for me just to see dependencies between variables. However either me or Maple or both are incapable of doing so. I am using Maple 13 by the way.

As one can see, the result is: "Warning, solutions may have been lost". I do not understand why, but it seems to be eqn 12. Just trying to solve it or isolate a variable from eqn12 in a sperate window is already being not possiblein Maple, even though it is a simple equation and easily solvable on paper.

I appreciate your help.

This isthe system:

> restart;
> rho[free] := 1.225;
                                   
> T[free] := 288.15;
                                
> p[free] := 1.01325*10^5;
                                            
> R := 287;
                                    
> y := 1.4;
                                    
> A[f] := 50;
                                   
> A[9] := 40;
                                   
> rho[free] := 1.225;
                                   
> c[p] := 1004;
                                   
> eta[is] := .85;
                                 
> eqn1 := F = m*v[9];
                              
> eqn2 := m = A[9]*rho[9]*v[9];
                            
> eqn3 := v[9] = M[9]*a[9];
                             

>eqn5 := a[9] = sqrt(y*R*T[9]);
                                              
> eqn6 := T[9]/T[3] = (1+((y-1)*(1/2))*M[9]^2)^(-y/(y-1));
               
> eqn7 := P[f] = c[p]*(T[3]-T[2])*rho[2]*A[f]*T[2];
                
> eqn8 := T[2] = T[free];
                           
> eqn9 := rho[2] = rho[free];
                          
> eqn10 := rho[9]/rho[3] = (1+((y-1)*(1/2))*M[9]^2)^(-1/(y-1));
              
> eqn11 := p[3] = rho[3]*R*T[3];
                       
> eqn12 := T[3]/T[2] = 1+[(p[3]/p[2])^((y-1)/y)-1]/eta[is];

> eqn13 := p[2] = p[free];
                                     
> solve({eqn1, eqn2, eqn3, eqn5, eqn6, eqn7, eqn8, eqn9, eqn10, eqn11, eqn12, eqn13});

Warning, solutions may have been lost