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