The problem“warning: Possibly spurious solutions.”in the symbolic solution with the function "solve".

Hi Guys:

I get two functions which are shown in the picture.

In the functions, the volume of w1_real,w2,t,sita,R,k,b,X,Y,Z are known. So,I use the equations to solve x,y.

Just like this:

The functions of F1 and F2 just like:

 F1 =R*cos(t*w2)*sin(sita) - x*(sin(t*w2)*sin(t*w1_real) - cos(t*w2)*cos(t*w1_real)*cos(sita)) - y*(cos(t*w1_real)*sin(t*w2) + cos(t*w2)*sin(t*w1_real)*cos(sita)) - X - cos(t*w2)*sin(sita)*(b + k*(x^2 + y^2)^(1/2))
 F2 =x*(cos(t*w2)*sin(t*w1_real) + cos(t*w1_real)*sin(t*w2)*cos(sita)) - Y + y*(cos(t*w2)*cos(t*w1_real) - sin(t*w2)*sin(t*w1_real)*cos(sita)) + R*sin(t*w2)*sin(sita) - sin(t*w2)*sin(sita)*(b + k*(x^2 + y^2)^(1/2))

So, I use function"solve".But i get a problem"warning: Possibly spurious solutions.".

Is there something wrong with my program code or the mathematical model？

Here is my program code.

syms w1_real w2 t sita R;
T=[-sin(w1_real.*t).*sin(w2.*t)+cos(w1_real.*t).*cos(w2.*t).*cos(sita)    -cos(w1_real.*t).*sin(w2.*t)-sin(w1_real.*t).*cos(w2.*t).*cos(sita)      -cos(w2.*t).*sin(sita)      R.*cos(w2.*t).*sin(sita);
   sin(w1_real.*t).*cos(w2.*t)+cos(w1_real.*t).*sin(w2.*t).*cos(sita)     cos(w1_real.*t).*cos(w2.*t)-sin(w1_real.*t).*sin(w2.*t).*cos(sita)       -sin(w2.*t).*sin(sita)      R.*sin(w2.*t).*sin(sita);
   cos(w1_real.*t).*sin(sita)                                             -sin(w1_real.*t).*sin(sita)                                              cos(sita)                   -R.*cos(sita);
   0                                                                      0                                                                        0                           1;];

syms x y k b X Y Z;
PXYZ=[X;Y;Z;1;];
Pxyz=[x;y;k*(x^2+y^2)^0.5+b;1;];

PXYZT=T*Pxyz;
F1=PXYZT(1)-PXYZ(1);
F2=PXYZT(2)-PXYZ(2);

equs=[F1,F2];

vars=[x y];

[S1,S2]=solve(equs,vars);