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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Updated on: 10-Oct-2022

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