Question

solve this problem of linear equation in two variable

Answer 1

The equations are:-

$\frac{x + y}{xy} = 2 \\ \\ \\ \frac{x}{xy} + \frac{y}{xy} = 2 \\ \\ \\ \frac{1}{y} +\frac{1}{x} = 2$

Second Equation is :-

$\frac{x - y}{xy} = 6 \\ \\ \\ \frac{x}{xy} - \frac{y}{xy} = 6 \\ \\ \\ \frac{1}{y} - \frac{1}{x} = 6$

$\rule{200}{2}$

Solving the two equations :-

$\frac{1}{y} + \frac{1}{x} = 2 \\ \\ \\ \frac{1}{y} - \frac{1}{x} = 6 \\ \\ \\ = = = = = = = = = \\ \\ \frac{2}{y} = 8 \\ \\y = \dfrac{2}{8} \\ \\ \\y =\dfrac{1}{4}$

$\rule{200}{2}$

Obtaining value of x

$\frac{1}{y} + \frac{1}{x} = 2 \\ \\ \\ \frac{1}{x} = 2 - \frac{1}{\dfrac{1}{4}} \\ \\ \frac{1}{x} =2-4 \\ \\ \\x = \frac{(-1)}{2}$

$\rule{200}{2}$