Solve {l}{ax+by=ab}{b+a=xy}

$$\left\{ \begin{array} { l } { a x + b y = a b } \\ { b + a = x y } \end{array} \right.$$

Solve for x, y (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{\frac{b\left(ab-4a-4b\right)}{a}}+b}{2}\text{, }y=\frac{a\left(-\sqrt{\frac{b\left(ab-4a-4b\right)}{a}}+b\right)}{2b}\text{; }x=\frac{-\sqrt{\frac{b\left(ab-4a-4b\right)}{a}}+b}{2}\text{, }y=\frac{a\left(\sqrt{\frac{b\left(ab-4a-4b\right)}{a}}+b\right)}{2b}\text{, }&b\neq 0\text{ and }a\neq 0\\x=0\text{, }y\neq 0\text{; }x\in \mathrm{C}\text{, }y=0\text{, }&b=0\text{ and }a=0\end{matrix}\right.$$

Solve for x, y

$$\left\{\begin{matrix}x=\frac{\sqrt{\frac{b\left(ab-4a-4b\right)}{a}}+b}{2}\text{, }y=\frac{a\left(-\sqrt{\frac{b\left(ab-4a-4b\right)}{a}}+b\right)}{2b}\text{; }x=\frac{-\sqrt{\frac{b\left(ab-4a-4b\right)}{a}}+b}{2}\text{, }y=\frac{a\left(\sqrt{\frac{b\left(ab-4a-4b\right)}{a}}+b\right)}{2b}\text{, }&\left(b\neq 0\text{ and }a\geq \frac{4b}{b-4}\text{ and }b\neq 4\text{ and }a<0\right)\text{ or }\left(a\geq \frac{4b}{b-4}\text{ and }a\neq 0\text{ and }b>4\right)\text{ or }\left(a\geq \frac{4b}{b-4}\text{ and }a\neq 0\text{ and }b<0\right)\text{ or }\left(b\geq 4\text{ and }a<0\right)\text{ or }\left(a<0\text{ and }b<0\right)\\x=0\text{, }y\neq 0\text{; }x\in \mathrm{R}\text{, }y=0\text{, }&b=0\text{ and }a=0\end{matrix}\right.$$