Solve {l}{ygeqx^2}{z^2=-x}{zleqx+t}

$$\left\{ \begin{array} { l } { y \geq x ^ { 2 } } \\ { z ^ { 2 } = - x } \\ { z \leq x + t } \end{array} \right.$$

Solve for x

$$x=-z^{2}$$

$$y\geq 0\text{ and }|z|\leq \sqrt[4]{y}\text{ and }t\geq z^{2}+z$$

Solve for z

$$\left\{\begin{matrix}z=-\sqrt{-x}\text{, }&\left(x>-t\text{ and }y\geq x^{2}\text{ and }x<0\right)\text{ or }\left(t\geq -\frac{1}{4}\text{ and }t\leq \frac{3}{4}\text{ and }y\geq \frac{1}{16}\text{ and }x=-\frac{1}{4}\right)\text{ or }\left(x>-t\text{ and }x\geq -t+\frac{\sqrt{4t+1}}{2}-\frac{1}{2}\text{ and }t\neq -\frac{1}{4}\text{ and }x\leq 0\text{ and }y\geq x^{2}\right)\text{ or }\left(x\geq -1\text{ and }x\leq 0\text{ and }t=0\text{ and }y\geq x^{2}\right)\text{ or }\left(x\geq -t-\frac{\sqrt{4t+1}}{2}-\frac{1}{2}\text{ and }x\leq -t+\frac{\sqrt{4t+1}}{2}-\frac{1}{2}\text{ and }t>-\frac{1}{4}\text{ and }y\geq x^{2}\text{ and }x<0\right)\\z=\sqrt{-x}\text{, }&\left(t=0\text{ and }y\geq 0\text{ and }x=0\right)\text{ or }\left(x>-t\text{ and }x\geq -t+\frac{\sqrt{4t+1}}{2}-\frac{1}{2}\text{ and }x\leq 0\text{ and }y\geq x^{2}\right)\end{matrix}\right.$$