Question

x+y/xy=2 x-y/xy=6 find the values of x and y​

Answer 1

Answer:

x=-1/2

y=1/4

Step-by-step explanation:

$\frac{x + y}{xy} = 2 \\ \frac{x - y}{xy} = 6$

$\frac{x + y}{xy} + \frac{x - y}{xy} = 2 + 6 \\ \frac{x + y + x - y}{xy} = 8$

$\frac{2x}{xy} = 8 \\ 2x = 8xy$

$\frac{1}{y} = \frac{8x}{2x } \\ \frac{1}{y} = 4$

$y = \frac{1}{4}$

$\frac{x + \frac{1}{4} }{x \frac{1}{4} } = 2 \\ x + \frac{1}{4} \times \frac{4}{x} = 2$

$\frac{4x + 1}{4} \times \frac{4}{x} = 2$

$4x + 1 = 2 \times \frac{x}{4} \times 4 \\ 4x + 1= 2x$

$4x - 2x = - 1 \\ 2x = - 1$

$x = \frac{ - 1}{2}$