Question

solve the following pair of equation by converting them as pair of linear equation x+y/xy=2 and x-y/xy=6

Answer 1

$\frac{x + y}{xy} = 2 \: \: \: or \: \: \: \frac{1}{x} + \frac{1}{y} = 2 \\ \frac{x - y}{xy} = 6 \: \: or \: \: \frac{1}{y} - \frac{1}{x} = 6 \\ taking \: \frac{1}{x} = u \: \: and \: \: \frac{1}{y} = v \\ u + v = 2\: \\ \: v - u = 6 \\ on \: solving \: \\ u = - 2 \\ v = 4 \\ x = \frac{ - 1}{2} \\ y = \frac{ 1}{4}$