Solve {l}{x^2+y^2leq4}{x^2+(y+1)^2geq1}{xleq0}

$$\left\{ \begin{array} { l } { x ^ { 2 } + y ^ { 2 } \leq 4 } \\ { x ^ { 2 } + ( y + 1 ) ^ { 2 } \geq 1 } \\ { x \leq 0 } \end{array} \right.$$

Solve for x

$$\left\{\begin{matrix}x\in \begin{bmatrix}-\sqrt{4-y^{2}},0\end{bmatrix}\text{, }&y>0\text{ and }y\leq 2\\x\in \begin{bmatrix}-\sqrt{4-y^{2}},-\sqrt{-y\left(y+2\right)}\end{bmatrix}\text{, }&y\geq -2\text{ and }y\leq 0\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y\in \begin{bmatrix}-\sqrt{4-x^{2}},-\sqrt{1-x^{2}}-1\end{bmatrix}\cup \begin{bmatrix}\sqrt{1-x^{2}}-1,\sqrt{4-x^{2}}\end{bmatrix}\text{, }&x\geq -1\text{ and }x\leq 0\\y\in \begin{bmatrix}-\sqrt{4-x^{2}},\sqrt{4-x^{2}}\end{bmatrix}\text{, }&x\geq -2\text{ and }x\leq -1\end{matrix}\right.$$