Solve {l}{r_{1}:3x-y=6}{r_{2}:-x-y=-2}

$$\left\{ \begin{array} { l } { r _ { 1 } : 3 x - y = 6 } \\ { r _ { 2 } : - x - y = - 2 } \end{array} \right.$$

Solve for x, y (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{144-3r_{1}r_{2}}+12}{r_{1}}\text{, }y=\frac{\sqrt{144-3r_{1}r_{2}}}{3}-2\text{, }&r_{1}\neq 0\\x=\frac{-\sqrt{144-3r_{1}r_{2}}+12}{r_{1}}\text{, }y=-\frac{\sqrt{144-3r_{1}r_{2}}}{3}-2\text{, }&r_{1}\neq 0\text{ and }r_{2}\neq 0\\x=\frac{r_{2}}{8}\text{, }y=-6\text{, }&r_{2}\neq 0\text{ and }r_{1}=0\end{matrix}\right.$$

Solve for x, y

$$\left\{\begin{matrix}x=\frac{\sqrt{144-3r_{1}r_{2}}+12}{r_{1}}\text{, }y=\frac{\sqrt{144-3r_{1}r_{2}}}{3}-2\text{, }&\left(r_{1}=\frac{48}{r_{2}}\text{ and }r_{2}\neq 0\right)\text{ or }\left(r_{1}\neq 0\text{ and }r_{1}\geq \frac{48}{r_{2}}\text{ and }r_{2}<0\right)\text{ or }\left(r_{1}\neq 0\text{ and }r_{1}\leq \frac{48}{r_{2}}\text{ and }r_{2}>0\right)\text{ or }\left(r_{1}\neq 0\text{ and }r_{2}=0\right)\\x=\frac{-\sqrt{144-3r_{1}r_{2}}+12}{r_{1}}\text{, }y=-\frac{\sqrt{144-3r_{1}r_{2}}}{3}-2\text{, }&\left(r_{1}=\frac{48}{r_{2}}\text{ and }r_{2}\neq 0\right)\text{ or }\left(r_{1}\neq 0\text{ and }r_{1}\geq \frac{48}{r_{2}}\text{ and }r_{2}<0\right)\text{ or }\left(r_{1}\neq 0\text{ and }r_{1}\leq \frac{48}{r_{2}}\text{ and }r_{2}>0\right)\\x=\frac{r_{2}}{8}\text{, }y=-6\text{, }&r_{2}\neq 0\text{ and }r_{1}=0\end{matrix}\right.$$