Solve {l}{Ix+y=11}{sqrt{y}+x=7}

$$\left. \begin{array} { l } { I x + y = 11 } \\ { \sqrt { y } + x = 7 } \end{array} \right.$$

Solve for x, y (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{I^{2}-28I+44}}{2}-\frac{I}{2}+7\text{, }y=\frac{\left(-\sqrt{I^{2}-28I+44}+I\right)^{2}}{4}\text{, }&I=\frac{11}{7}\text{ or }arg(\frac{-\sqrt{I^{2}-28I+44}+I}{2})<\pi \\x=-\frac{\sqrt{I^{2}-28I+44}}{2}-\frac{I}{2}+7\text{, }y=\frac{\left(\sqrt{I^{2}-28I+44}+I\right)^{2}}{4}\text{, }&arg(\frac{\sqrt{I^{2}-28I+44}+I}{2})<\pi \end{matrix}\right.$$

Solve for x, y

$$\left\{\begin{matrix}x=\frac{\sqrt{I^{2}-28I+44}}{2}-\frac{I}{2}+7\text{, }y=\frac{\left(-\sqrt{I^{2}-28I+44}+I\right)^{2}}{4}\text{, }&I\geq 2\sqrt{38}+14\text{ or }\left(I\geq \frac{11}{7}\text{ and }I\leq 14-2\sqrt{38}\right)\\x=-\frac{\sqrt{I^{2}-28I+44}}{2}-\frac{I}{2}+7\text{, }y=\frac{\left(\sqrt{I^{2}-28I+44}+I\right)^{2}}{4}\text{, }&I\geq 2\sqrt{38}+14\text{ or }I\leq 14-2\sqrt{38}\end{matrix}\right.$$