Question: Solving a system of non-linear equations for different parameters

I have the following system of non-linear equations and want to find their solutions experimenting with my parameters. I also want to restrict the solutions to be non-negative. I have done the following, but i am sure it exist a more efficient way. Can somone help on this? 

eqns := [A = (gr_c+delta)*kh^(1-alpha)/sav_rate, theta = Rk*(Rh-Rk)/(gamma*((Rh-Rk)^2+sigma^2)), theta = 1*1+kh, Rk = 1+rk-delta, Rh = 1+rh-delta, rk = A*alpha*kh^(alpha-1), rh = A*(1-alpha)*kh^alpha, sigma = sigmay/theta, varrho = Rap^((eps-1)*eps/(1-gamma)), Rap = Rk^(1-gamma)+(1-gamma)*Rk^(-gamma)*theta*(Rh-Rk)-.5*Rk^(-gamma-1)*gamma*(1-gamma)*theta^2*((Rh-Rk)^2+sigma^2), R = Rk+theta*(Rh-Rk), beta = ((1+gr_c)/R)^(1/eps)/varrho];
print(`output redirected...`); # input placeholder
[
[
[
[
[ (1 - alpha)
[ (gr_c + delta) kh
[A = ----------------------------,
[ sav_rate
[

Rk (Rh - Rk)
theta = ---------------------------, theta = 1 + kh,
/ 2 2\
gamma \(Rh - Rk) + sigma /

Rk = 1 + rk - delta, Rh = 1 + rh - delta,

(alpha - 1) alpha
rk = A alpha kh , rh = A (1 - alpha) kh ,

/(eps - 1) eps\
|-------------|
sigmay \ 1 - gamma /
sigma = ------, varrho = Rap , Rap =
theta

(1 - gamma) (-gamma)
Rk + (1 - gamma) Rk theta (Rh - Rk) - 0.5

(-gamma - 1) 2 / 2 2\
Rk gamma (1 - gamma) theta \(Rh - Rk) + sigma /,

/ 1 \]
|---|]
\eps/]
/1 + gr_c\ ]
|--------| ]
\ R / ]
R = Rk + theta (Rh - Rk), beta = ---------------]
varrho ]
]
vals := [alpha = .36, delta = 0.6e-1, sigmay = sqrt(0.313e-1), gamma = 3, eps = .5, gr_c = 0.2e-1, sav_rate = .23];
eval(eqns, vals);
print(`output redirected...`); # input placeholder
[
[
[
[ 0.64 Rk (Rh - Rk)
[A = 0.3478260870 kh , theta = -----------------------,
[ / 2 2\
[ 3 \(Rh - Rk) + sigma /

0.36 A
theta = 1 + kh, Rk = 0.94 + rk, Rh = 0.94 + rh, rk = ------,
0.64
kh

0.36 0.1769180601
rh = 0.64 A kh , sigma = ------------,
theta

0.1250000000
varrho = Rap ,

1 2 theta (Rh - Rk)
Rap = --- - -----------------
2 3
Rk Rk

2 / 2 2\
3.0 theta \(Rh - Rk) + sigma /
+ --------------------------------, R = Rk + theta (Rh - Rk),
4
Rk

2.000000000]
/1\ ]
1.0404 |-| ]
\R/ ]
beta = ---------------------]
varrho ]
]
eqns := [A = .3478260870*kh^.64, theta = (1/3)*Rk*(Rh-Rk)/((Rh-Rk)^2+sigma^2), theta = 1+kh, Rk = .94+rk, Rh = .94+rh, rk = .36*A/kh^.64, rh = .64*A*kh^.36, sigma = .1769180601/theta, varrho = Rap^.1250000000, Rap = 1/Rk^2-2*theta*(Rh-Rk)/Rk^3+3.0*theta^2*((Rh-Rk)^2+sigma^2)/Rk^4, R = Rk+theta*(Rh-Rk), beta = 1.0404*(1/R)^2.000000000/varrho];
print(`output redirected...`); # input placeholder
[
[
[
[ 0.64 Rk (Rh - Rk)
[A = 0.3478260870 kh , theta = -----------------------,
[ / 2 2\
[ 3 \(Rh - Rk) + sigma /

0.36 A
theta = 1 + kh, Rk = 0.94 + rk, Rh = 0.94 + rh, rk = ------,
0.64
kh

0.36 0.1769180601
rh = 0.64 A kh , sigma = ------------,
theta

0.1250000000
varrho = Rap ,

1 2 theta (Rh - Rk)
Rap = --- - -----------------
2 3
Rk Rk

2 / 2 2\
3.0 theta \(Rh - Rk) + sigma /
+ --------------------------------, R = Rk + theta (Rh - Rk),
4
Rk

2.000000000]
/1\ ]
1.0404 |-| ]
\R/ ]
beta = ---------------------]
varrho ]
]

solve(eqns, [Rk, Rh, varrho, Rap, beta, R, A, sigma, theta, rk, rh, kh]);