Solve the following system of equations:
$\frac{(x\ +\ y)}{xy}\ =\ 2$
$\frac{(x\ –\ y)}{xy}\ =\ 6$

Given:

The given system of equations is:

$\frac{(x\ +\ y)}{xy}\ =\ 2$

$\frac{(x\ –\ y)}{xy}\ =\ 6$

To do:

We have to solve the given system of equations.

Solution:

The given system of equations can be written as,

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

$x+y=2(xy)$

$x+y=2xy$---(i)

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

$x-y=6(xy)$

$x-y=6xy$---(ii)

Adding equations (i) and (ii), we get,

$x+y+x-y=2xy+6xy$

$2x=8xy$

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

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

Using $y=\frac{1}{4}$ in equation (i), we get,

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

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

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

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

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

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

Therefore, the solution of the given system of equations is $x=-\frac{1}{2}$ and $y=\frac{1}{4}$. 

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Updated on: 10-Oct-2022

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