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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