Solve {l}{x^2+y^2>4}{y<x+1}

$$\left\{ \begin{array} { l } { x ^ { 2 } + y ^ { 2 } > 4 } \\ { y < x + 1 } \end{array} \right.$$

Solve for x

$$\left\{\begin{matrix}x\in \left(y-1,-\sqrt{4-y^{2}}\right)\text{, }&y\geq -2\text{ and }y<\frac{1-\sqrt{7}}{2}\\x>y-1\text{, }&|y|>2\text{ or }\left(y\geq \frac{\sqrt{7}+1}{2}\text{ and }y\leq 2\right)\\x>\sqrt{4-y^{2}}\text{, }&\left(y>\frac{1-\sqrt{7}}{2}\text{ and }y<\frac{\sqrt{7}+1}{2}\text{ and }|y|\leq 2\right)\text{ or }\left(y\geq -2\text{ and }y<\frac{1-\sqrt{7}}{2}\right)\text{ or }\left(y<1\text{ and }|y|\leq 2\right)\text{ or }\left(y\leq 1\text{ and }y>-2\text{ and }|y|\leq 2\right)\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y\in \left(\sqrt{4-x^{2}},x+1\right)\text{, }&x>\frac{\sqrt{7}-1}{2}\text{ and }x\leq 2\\y<x+1\text{, }&|x|>2\text{ or }\left(x\geq -2\text{ and }x\leq \frac{-\sqrt{7}-1}{2}\right)\\y<-\sqrt{4-x^{2}}\text{, }&\left(x>\frac{-\sqrt{7}-1}{2}\text{ and }x<\frac{\sqrt{7}-1}{2}\text{ and }|x|\leq 2\right)\text{ or }\left(x>\frac{\sqrt{7}-1}{2}\text{ and }x\leq 2\right)\text{ or }\left(x>-1\text{ and }|x|\leq 2\right)\text{ or }\left(x\geq -1\text{ and }x<2\text{ and }|x|\leq 2\right)\end{matrix}\right.$$