Solve {c}{x+y^2=5}{x^2+y=3}

$$\left. \begin{array} { c } { x + y ^ { 2 } = 5 } \\ { x ^ { 2 } + y = 3 } \end{array} \right.$$

Solve for x, y

$$x=1\text{, }y=2$$

$$x=\frac{-4\left(\sqrt{22}\cos(\frac{\arccos(\frac{173\sqrt{22}}{968})}{3})-1\right)^{2}+45}{9}\approx -0.772865558\text{, }y=\frac{2\left(\sqrt{22}\cos(\frac{\arccos(\frac{173\sqrt{22}}{968})}{3})-1\right)}{3}\approx 2.40267883$$

$$x=\frac{-\left(\sqrt{22}\cos(\frac{\arccos(\frac{173\sqrt{22}}{968})}{3})+\sqrt{66}\sin(\frac{\arccos(\frac{173\sqrt{22}}{968})}{3})+2\right)^{2}+45}{9}\approx -2.391382381\text{, }y=\frac{-\sqrt{22}\cos(\frac{\arccos(\frac{173\sqrt{22}}{968})}{3})-\sqrt{66}\sin(\frac{\arccos(\frac{173\sqrt{22}}{968})}{3})-2}{3}\approx -2.71870969$$

$$x=\frac{-\left(\sqrt{66}\sin(\frac{\arccos(\frac{173\sqrt{22}}{968})}{3})-\sqrt{22}\cos(\frac{\arccos(\frac{173\sqrt{22}}{968})}{3})-2\right)^{2}+45}{9}\approx 2.164247938\text{, }y=\frac{\sqrt{66}\sin(\frac{\arccos(\frac{173\sqrt{22}}{968})}{3})-\sqrt{22}\cos(\frac{\arccos(\frac{173\sqrt{22}}{968})}{3})-2}{3}\approx -1.683969139$$