Solve {l}{5x^2+2y^2leq10}{ygeqx^2-2x+1}

$$\left. \begin{array} { l } { 5 x ^ { 2 } + 2 y ^ { 2 } \leq 10 } \\ { y \geq x ^ { 2 } - 2 x + 1 } \end{array} \right.$$

Solve for x

$$\left\{\begin{matrix}x=1\text{, }&y\geq 0\text{ and }y\leq \frac{\sqrt{10}}{2}\\x\in \begin{bmatrix}-\frac{\sqrt{50-10y^{2}}}{5},\sqrt{y}+1\end{bmatrix}\text{, }&-\sqrt{-\frac{2y^{2}}{5}+2}\geq -\sqrt{y}+1\text{ and }\sqrt{y}+1<\sqrt{-\frac{2y^{2}}{5}+2}\text{ and }y\leq \sqrt{5}\text{ and }y>0\\x=\frac{\sqrt{50-10y^{2}}}{5}\text{, }&y\leq \sqrt{5}\text{ and }\sqrt{-\frac{2y^{2}}{5}+2}=-\sqrt{y}+1\text{ and }y>0\\x\in \begin{bmatrix}-\sqrt{y}+1,\frac{\sqrt{50-10y^{2}}}{5}\end{bmatrix}\text{, }&-\sqrt{y}+1<\sqrt{-\frac{2y^{2}}{5}+2}\text{ and }-\sqrt{-\frac{2y^{2}}{5}+2}<-\sqrt{y}+1\text{ and }\sqrt{-\frac{2y^{2}}{5}+2}\leq \sqrt{y}+1\text{ and }y\leq \sqrt{5}\text{ and }y>0\\x\in \begin{bmatrix}-\frac{\sqrt{50-10y^{2}}}{5},\frac{\sqrt{50-10y^{2}}}{5}\end{bmatrix}\text{, }&-\sqrt{-\frac{2y^{2}}{5}+2}\geq -\sqrt{y}+1\text{ and }\sqrt{-\frac{2y^{2}}{5}+2}\leq \sqrt{y}+1\text{ and }y\leq \sqrt{5}\text{ and }y>0\\x\in \begin{bmatrix}-\sqrt{y}+1,\sqrt{y}+1\end{bmatrix}\text{, }&-\sqrt{-\frac{2y^{2}}{5}+2}<-\sqrt{y}+1\text{ and }\sqrt{y}+1<\sqrt{-\frac{2y^{2}}{5}+2}\text{ and }y\leq \sqrt{5}\text{ and }y>0\end{matrix}\right.$$

Solve for y

$$y\in \begin{bmatrix}\left(x-1\right)^{2},\frac{\sqrt{20-10x^{2}}}{2}\end{bmatrix}\text{, }|x|\leq \sqrt{2}\text{ and }\left(x-1\right)^{2}\leq \sqrt{-\frac{5x^{2}}{2}+5}$$