\left\{ \begin{array} { l } { x ^ { 2 } + y ^ { 2 } \leq 9 } \\ { x ^ { 2 } + y ^ { 2 } - 4 x - 6 y + 4 \geq 0 } \end{array} \right.
Solve for x
\left\{\begin{matrix}x\in \begin{bmatrix}\sqrt{y\left(6-y\right)}+2,\sqrt{9-y^{2}}\end{bmatrix}\text{, }&y\geq 0\text{ and }y\leq -\frac{\sqrt{299}}{13}+\frac{3}{2}\\x\in \begin{bmatrix}-\sqrt{9-y^{2}},-\sqrt{y\left(6-y\right)}+2\end{bmatrix}\text{, }&\left(y>0\text{ and }y\leq \frac{5}{6}\right)\text{ or }\left(y>-\frac{\sqrt{299}}{13}+\frac{3}{2}\text{ and }y<\frac{\sqrt{299}}{13}+\frac{3}{2}\right)\text{ or }\left(y\geq 0\text{ and }y<\frac{5}{6}\right)\\x=-\sqrt{y\left(6-y\right)}+2\text{, }&y=\frac{\sqrt{299}}{13}+\frac{3}{2}\\x\in \begin{bmatrix}-\sqrt{9-y^{2}},\sqrt{9-y^{2}}\end{bmatrix}\text{, }&y\geq -3\text{ and }y\leq 0\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y\in \begin{bmatrix}-\sqrt{9-x^{2}},\sqrt{9-x^{2}}\end{bmatrix}\text{, }&\left(x\geq -3\text{ and }x\leq -1\right)\text{ or }\left(x\geq \frac{3\sqrt{299}}{26}+1\text{ and }x\leq 3\right)\text{ or }\left(x\geq -1\text{ and }x\leq -\frac{3\sqrt{299}}{26}+1\right)\\y\in \begin{bmatrix}-\sqrt{9-x^{2}},-\sqrt{-\left(x-5\right)\left(x+1\right)}+3\end{bmatrix}\text{, }&x>-\frac{3\sqrt{299}}{26}+1\text{ and }x<\frac{3\sqrt{299}}{26}+1\text{ and }|x|\leq 3\end{matrix}\right.
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