Solve for x (complex solution)
x=\frac{-\sqrt{3\left(1-y\right)\left(y+3\right)}+y+3}{2}
x=-y
x=\frac{\sqrt{3\left(1-y\right)\left(y+3\right)}+y+3}{2}
Solve for y (complex solution)
y=\frac{\sqrt{-3\left(x-3\right)\left(x+1\right)}+x-3}{2}
y=\frac{-\sqrt{-3\left(x-3\right)\left(x+1\right)}+x-3}{2}
y=-x
Solve for x
\left\{\begin{matrix}\\x=-y\text{, }&\text{unconditionally}\\x=\frac{\sqrt{3\left(1-y\right)\left(y+3\right)}+y+3}{2}\text{; }x=\frac{-\sqrt{3\left(1-y\right)\left(y+3\right)}+y+3}{2}\text{, }&y\geq -3\text{ and }y\leq 1\end{matrix}\right.
Solve for y
\left\{\begin{matrix}\\y=-x\text{, }&\text{unconditionally}\\y=\frac{\sqrt{3\left(3-x\right)\left(x+1\right)}+x-3}{2}\text{; }y=\frac{-\sqrt{3\left(3-x\right)\left(x+1\right)}+x-3}{2}\text{, }&x\geq -1\text{ and }x\leq 3\end{matrix}\right.
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