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Solve the following system of equations:
$\frac{7x-2y}{xy}=5$$\frac{8x+7y}{xy}=15$
Given:
The given system of equations is:
$\frac{7x-2y}{xy}=5$
$\frac{8x+7y}{xy}=15$
To do:
We have to solve the given system of equations.
Solution:
The given system of equations can be written as,
$\frac{7x-2y}{xy}=5$
$7x-2y=5(xy)$
$7x-2y=5xy$
$7(7x-2y)=7(5xy)$ (Multiplying by 7 on both sides)
$49x-14y=35xy$---(i)
$\frac{8x+7y}{xy}=15$
$8x+7y=15(xy)$
$8x+7y=15xy$
$2(8x+7y)=2(15xy)$
$16x+14y=30xy$---(ii)
Adding equations (i) and (ii), we get,
$49x-14y+16x+14y=35xy+30xy$
$65x=65xy$
$\frac{xy}{x}=\frac{65}{65}$
$y=1$
Using $y=1$ in equation (i), we get,
$49x-14(1)=35x(1)$
$49x-14=35x$
$49x-35x=14$
$14x=14$
$x=\frac{14}{14}$
$x=1$
Therefore, the solution of the given system of equations is $x=1$ and $y=1$.
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