Solve for x
x=\left(z-\sqrt[3]{y}\right)^{2}
z-\sqrt[3]{y}\geq 0
Solve for y
y=\left(z-\sqrt{x}\right)^{3}
x\geq 0
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\sqrt{x}+\sqrt[3]{y}=z
Swap sides so that all variable terms are on the left hand side.
\sqrt{x}=z-\sqrt[3]{y}
Subtract \sqrt[3]{y} from both sides.
x=\left(z-\sqrt[3]{y}\right)^{2}
Square both sides of the equation.
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