Why does Sage not find any solutions using .solve()?

edit

Hello everyone,

please consider this attempt to solve simultaneous equations:

P,M,R,rho,kappa,T,F,n = var('P, M, R, rho, kappa, T, F, n')

eqns = [
P==M^2*R^-4,
R^3==M*rho^-1,
T^4==M*kappa*F*R^-4,
F==M*rho*T^n,
P==rho*T,
kappa==rho*T^(-7/2),
n==4
]

eqns

assume(P>0,M>0,R>0,rho>0,T>0,F>0,kappa>0)

sols = solve(eqns,(F,R,T))
sols

(returns [])

I would like to understand why Sage can not arrive at a relation for F,M,T (and n) which I was able to do by hand. Is solve inappropriate for isolating one or more variables from a set of equations?

Thank you for your help!