Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{\sqrt{6-2y^{2}}+2y}{3}\text{, }&y=\sqrt{2}\text{ or }arg(\frac{-\sqrt{24-8y^{2}}+2y}{3})<\pi \\x=\frac{-\sqrt{6-2y^{2}}+2y}{3}\text{, }&y=-\sqrt{2}\text{ or }arg(\frac{\sqrt{24-8y^{2}}+2y}{3})<\pi \end{matrix}\right.
Solve for y (complex solution)
y=\frac{\sqrt{4-2x^{2}}}{2}+x
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{6-2y^{2}}+2y}{3}\text{, }&y\geq \sqrt{2}\text{ and }y\leq \sqrt{3}\\x=\frac{-\sqrt{6-2y^{2}}+2y}{3}\text{, }&y=-\sqrt{2}\text{ or }\left(y\geq -\sqrt{2}\text{ and }|y|\leq \sqrt{3}\right)\end{matrix}\right.
Solve for y
y=\frac{\sqrt{4-2x^{2}}}{2}+x
|x|\leq \sqrt{2}
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