Question: Solving simultaneous equations

Could someone show me how to solve the following equations for real x, y and z.

Thanks

x^2 + 2yz^2 = 0,

y^2  - 3xz = 0, 

1/3*x*y^2 + 2*y*z^3 = 0,

-1/3*y^4 - 6yz^4 = 0.

 

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