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**1. Homework Statement**

Hello there, I'm having trouble solving the following system:

x^2 + y^2 = 1 (I)

x^2 + z^2 + x*z*sqrt(3) = 4 (II)

y^2 + z^2 + z*y = 3 (III)

**2. Homework Equations**

**3. The Attempt at a Solution**

Working on (I):

y^2 = 1 - x^2

Working on (III):

(1 - x^2) + z^2 + z*sqrt(1 - x^2) = 3

z = (2 + x^2)/(z + sqrt(1 - x^2))

And here starts the problem, because I can't isolate the 'z', so I can't really move on.