3 equations for 3 variables -- simple right?

Algebra Level 1

Let x, y and z be positive real numbers.

Given 3 equations:

1) $$x^{2} + y + z = 6$$

2) $$x + y^{2} + z = 8$$

3) $$x + y + z^{2} = 12$$

Compute $$x^{7} + y^{4} + z$$

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