System of Equations with Unknown Variables

[Je m'appelle]

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)

Homework Equations

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.

 

[Gib Z]

It may look ugly in the end, but to isolate z after you've started working on eqn 3, treat it as a quadratic equation in z.

 

[Je m'appelle]

It may look ugly in the end, but to isolate z after you've started working on eqn 3, treat it as a quadratic equation in z.

Thank you, I'll try it.