Solve {l}{x^2-xy+y^2=1}{x^2+xy-4y^2=2}

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

Solve for x, y (complex solution)

$$x=\frac{\sqrt{19}\left(-\sqrt{-3\sqrt{19}e^{\left(\arctan(\frac{\sqrt{15}}{2})+\pi \right)i}+76}+\sqrt[4]{19}e^{\frac{\left(\arctan(\frac{\sqrt{15}}{2})+\pi \right)i}{2}}\right)}{38}\approx -1.165890146+0.131128067i\text{, }y=\frac{19^{\frac{3}{4}}e^{\frac{\left(\arctan(\frac{\sqrt{15}}{2})+\pi \right)i}{2}}}{19}\approx -0.249151135+0.409071443i$$

$$x=\frac{\sqrt{19}\left(-\sqrt{-3\sqrt{19}e^{-\arctan(\frac{\sqrt{15}}{2})i+\pi i}+76}+\sqrt[4]{19}e^{\frac{-\arctan(\frac{\sqrt{15}}{2})i+\pi i}{2}}\right)}{38}\approx 1.165890146+0.131128067i\text{, }y=\frac{19^{\frac{3}{4}}e^{\frac{-\arctan(\frac{\sqrt{15}}{2})i+\pi i}{2}}}{19}\approx 0.249151135+0.409071443i$$

$$x=\frac{\sqrt{19}\left(\sqrt{-3\sqrt{19}e^{\arctan(\frac{\sqrt{15}}{2})i+3\pi i}+76}+\sqrt[4]{19}e^{\frac{\arctan(\frac{\sqrt{15}}{2})i+3\pi i}{2}}\right)}{38}\approx 1.165890146-0.131128067i\text{, }y=\frac{19^{\frac{3}{4}}e^{\frac{\arctan(\frac{\sqrt{15}}{2})i+3\pi i}{2}}}{19}\approx 0.249151135-0.409071443i$$

$$x=\frac{\sqrt{19}\left(\sqrt{-3\sqrt{19}e^{-\arctan(\frac{\sqrt{15}}{2})i+3\pi i}+76}+\sqrt[4]{19}e^{\frac{-\arctan(\frac{\sqrt{15}}{2})i+3\pi i}{2}}\right)}{38}\approx -1.165890146-0.131128067i\text{, }y=\frac{19^{\frac{3}{4}}e^{\frac{-\arctan(\frac{\sqrt{15}}{2})i+3\pi i}{2}}}{19}\approx -0.249151135-0.409071443i$$