Question: plot solution of a system with parameter

I have a nonlinear algebraic system with x ,y unknowns and beta parameter (0<beta<1); I want to plot in 3d the triplets (x,y,beta), where x and y are the solution of system for ten different values of beta.

For now I am able only to solve the system with fsolve, but I don't want to copy the solutions with copy and paste, because in the future I have to give to beta much more values than 10. Can anyone help me, please? This is the program:

restart:with(plots):
alpha:=Pi/3:
mu:=0.1:
rs:=((x+mu)^2+y^2)^0.5:
re:=((x+mu-1)^2+y^2)^0.5:
Q:=beta/10*(1-mu)*(cos(alpha))^2:
S:=(x+mu)*cos(alpha)+y*sin(alpha):
T:=-(x+mu)*sin(alpha)+y*cos(alpha):
eq1:=(1-mu)*(x+mu)/rs^3+mu*(x-mu+1)/re^3-x=Q*S/rs^3:
eq2:=(1-mu)*y/rs^3+mu*y/re^3-y=Q*T/rs^3:
for beta from 0 to 10 do fsolve({eq1,eq2}, {x,y}) end do;