Solve L_{1}:2x+3y=6text{and}L_{2}:x+y=-1

$$L _ { 1 } : 2 x + 3 y = 6 \text { and } L _ { 2 } : x + y = - 1$$

Solve for x, y (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{6L_{1}L_{2}+81}+9}{L_{1}}\text{, }y=-\frac{\sqrt{6L_{1}L_{2}+81}}{6}+\frac{1}{2}\text{, }&L_{1}\neq 0\\x=\frac{-\sqrt{6L_{1}L_{2}+81}+9}{L_{1}}\text{, }y=\frac{\sqrt{6L_{1}L_{2}+81}}{6}+\frac{1}{2}\text{, }&L_{1}\neq 0\text{ and }L_{2}\neq 0\\x=-\frac{L_{2}}{3}\text{, }y=2\text{, }&L_{2}\neq 0\text{ and }L_{1}=0\end{matrix}\right.$$

Solve for x, y

$$\left\{\begin{matrix}x=\frac{\sqrt{6L_{1}L_{2}+81}+9}{L_{1}}\text{, }y=-\frac{\sqrt{6L_{1}L_{2}+81}}{6}+\frac{1}{2}\text{, }&\left(L_{1}=-\frac{27}{2L_{2}}\text{ and }L_{2}\neq 0\right)\text{ or }\left(L_{1}\neq 0\text{ and }L_{1}\geq -\frac{27}{2L_{2}}\text{ and }L_{2}>0\right)\text{ or }\left(L_{1}\neq 0\text{ and }L_{1}\leq -\frac{27}{2L_{2}}\text{ and }L_{2}<0\right)\text{ or }\left(L_{1}\neq 0\text{ and }L_{2}=0\right)\\x=\frac{-\sqrt{6L_{1}L_{2}+81}+9}{L_{1}}\text{, }y=\frac{\sqrt{6L_{1}L_{2}+81}}{6}+\frac{1}{2}\text{, }&\left(L_{1}=-\frac{27}{2L_{2}}\text{ and }L_{2}\neq 0\right)\text{ or }\left(L_{1}\neq 0\text{ and }L_{1}\geq -\frac{27}{2L_{2}}\text{ and }L_{2}>0\right)\text{ or }\left(L_{1}\neq 0\text{ and }L_{1}\leq -\frac{27}{2L_{2}}\text{ and }L_{2}<0\right)\\x=-\frac{L_{2}}{3}\text{, }y=2\text{, }&L_{2}\neq 0\text{ and }L_{1}=0\end{matrix}\right.$$