Solve {l}{2x^2+y-y^2=0}{3x^2+2xy+y^2=2}

$$\left. \begin{array} { l } { 2 x ^ { 2 } + y - y ^ { 2 } = 0 } \\ { 3 x ^ { 2 } + 2 x y + y ^ { 2 } = 2 } \end{array} \right.$$

Solve for x, y

$$x=-\frac{\sqrt{2\left(3\sqrt{371}\sin(\frac{\arccos(\frac{2997\sqrt{1113}}{137641})}{3})+\sqrt{1113}\cos(\frac{\arccos(\frac{2997\sqrt{1113}}{137641})}{3})-12\right)\left(3\sqrt{371}\sin(\frac{\arccos(\frac{2997\sqrt{1113}}{137641})}{3})+\sqrt{1113}\cos(\frac{\arccos(\frac{2997\sqrt{1113}}{137641})}{3})+39\right)}}{102}\approx -0.756740638\text{, }y=\frac{3\sqrt{371}\sin(\frac{\arccos(\frac{2997\sqrt{1113}}{137641})}{3})+\sqrt{1113}\cos(\frac{\arccos(\frac{2997\sqrt{1113}}{137641})}{3})+39}{51}\approx 1.681233587$$

$$x=-\frac{\sqrt{\left(2\sqrt{1113}\cos(\frac{\arccos(\frac{2997\sqrt{1113}}{137641})}{3})-39\right)\left(\sqrt{1113}\cos(\frac{\arccos(\frac{2997\sqrt{1113}}{137641})}{3})+6\right)}}{51}\approx -0.614076154\text{, }y=\frac{-2\sqrt{1113}\cos(\frac{\arccos(\frac{2997\sqrt{1113}}{137641})}{3})+39}{51}\approx -0.502087344$$

$$x=\frac{\sqrt{2\left(\sqrt{1113}\cos(\frac{\arccos(\frac{2997\sqrt{1113}}{137641})}{3})-3\sqrt{371}\sin(\frac{\arccos(\frac{2997\sqrt{1113}}{137641})}{3})-12\right)\left(\sqrt{1113}\cos(\frac{\arccos(\frac{2997\sqrt{1113}}{137641})}{3})-3\sqrt{371}\sin(\frac{\arccos(\frac{2997\sqrt{1113}}{137641})}{3})+39\right)}}{102}\approx 0.253169733\text{, }y=\frac{\sqrt{1113}\cos(\frac{\arccos(\frac{2997\sqrt{1113}}{137641})}{3})-3\sqrt{371}\sin(\frac{\arccos(\frac{2997\sqrt{1113}}{137641})}{3})+39}{51}\approx 1.114971404$$

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