System of 3 equations with 3 variables

I have this system of 3 equations that contain 3 variables:

$\displaystyle 900x^4 + 90y^3 - z^3 - 5000 = 0$

$\displaystyle 600x^2 - 20y^3 - z^2 + 13000 = 0$

$\displaystyle 500x - 20y^2 + z - 600 = 0$

Approximate solutions are:

$\displaystyle x \approx 5.1293908$

$\displaystyle y \approx 10.1340453$

$\displaystyle z \approx 89.2820764$

OR

$\displaystyle x \approx 37.2632316$

$\displaystyle y \approx -31.0102185$

$\displaystyle z \approx 1201.0572216$

How do I solve this system of equations?

One set of solutions is good enough.

Please show all the steps you make.

Thanks. :)