Solve {l}{y=kx+2k+3}{y^2=gx}

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

Solve for x, y (complex solution)

$$\left\{\begin{matrix}x=\frac{-\sqrt{g\left(g-8k^{2}-12k\right)}-4k^{2}+g-6k}{2k^{2}}\text{, }y=\frac{-\sqrt{g\left(g-8k^{2}-12k\right)}+g}{2k}\text{; }x=\frac{\sqrt{g\left(g-8k^{2}-12k\right)}-4k^{2}+g-6k}{2k^{2}}\text{, }y=\frac{\sqrt{g\left(g-8k^{2}-12k\right)}+g}{2k}\text{, }&k\neq 0\\x=\frac{9}{g}\text{, }y=3\text{, }&k=0\text{ and }g\neq 0\end{matrix}\right.$$

Solve for x, y

$$\left\{\begin{matrix}x=\frac{-\sqrt{g\left(g-8k^{2}-12k\right)}-4k^{2}+g-6k}{2k^{2}}\text{, }y=\frac{-\sqrt{g\left(g-8k^{2}-12k\right)}+g}{2k}\text{; }x=\frac{\sqrt{g\left(g-8k^{2}-12k\right)}-4k^{2}+g-6k}{2k^{2}}\text{, }y=\frac{\sqrt{g\left(g-8k^{2}-12k\right)}+g}{2k}\text{, }&k\neq 0\text{ and }\left(k\geq -\frac{\sqrt{\left(2g+9\right)g^{2}}+3g}{4g}\text{ or }g\leq -\frac{9}{2}\text{ or }g=0\text{ or }k\leq \frac{\sqrt{\left(2g+9\right)g^{2}}-3g}{4g}\right)\text{ and }\left(k\geq -\frac{\sqrt{\left(2g+9\right)g^{2}}+3g}{4g}\text{ or }g\leq 0\right)\text{ and }\left(k\leq \frac{\sqrt{\left(2g+9\right)g^{2}}-3g}{4g}\text{ or }g\leq 0\right)\\x=\frac{9}{g}\text{, }y=3\text{, }&k=0\text{ and }g\neq 0\end{matrix}\right.$$