Question

x+y/xy=2 and x-y/xy=6

Answer 1

$\begin{cases}\frac{x+y}{xy}=2\\\frac{x-y}{xy}=6\\\end{cases}\\\begin{cases}\frac{1}{x}+\frac{1}{y}=2\\\frac{1}{y}-\frac{1}{x}=6\\\end{cases}\\\text{Add the two equations,}\\\frac{2}{y}=8\\y=\frac{1}{4}\\\text{Put the value of y in first equation,}\\\frac{1}{y}+4=2\\\frac{1}{y}=-2\\y=-\frac{1}{2}$