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Here is an approach using Sympy.

from sympy.solvers import solve
from sympy import Symbol
x=Symbol('x')
y=Symbol('y')
z=Symbol('z')

K=4.48e-13
xi=0.75
yi=0
zi=0

eq1=y**2*z/x**2-K
eq2=xi+yi-(x+y)
eq3=2*xi+yi+2*zi-(2*x+y+2*z)

print eq1,eq2,eq3

ans=solve([eq1,eq2,eq3],x,y,z)
print ans