Question

Solve the Equation:

1/2x -1/y = -1
1/x +1/2y = 8

Answer 1

hy



hope it helps u...

Answer 2

The value of x and y is $\frac{1}{6}\ {and}\ \frac{1}{4}$.  

To find:

Solve the Equation: $\frac{1}{2 x}-\frac{1}{y}=-1 \text { and } \frac{1}{x}+\frac{1}{2 y}=8=?$

Solution:

Given: $\frac{1}{2 x}-\frac{1}{y}=-1 \text { and } \frac{1}{x}+\frac{1}{2 y}=8$

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

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

$y-2 x=-2 x y$

$2 \mathrm{x}-\mathrm{y}=2 \mathrm{xy} \ldots \ldots \ldots (1)$

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

$\frac{2 y+x}{2 x y}=8$

$2 y+x=16 x y$

$x+2 y=16 x y \dots \ldots \ldots \ldots(2)$

Multiplying equation (1) by 2 and then adding it to equation (2), we get

$5 \mathrm{x}=20 \mathrm{xy}$

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

Replacing the value of $y=\frac{1}{4}$ in equation (1),

$2 x-y=2 x y$

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

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

$6 \mathrm{x}=1$

$x=\frac{1}{6}$