Solve the following system of equations:
$\frac{xy}{x+y} =\frac{6}{5}$
$\frac{xy}{y-x}=6$

Given:

The given system of equations is:

$\frac{xy}{x+y} =\frac{6}{5}$

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

To do:

We have to solve the given system of equations.

Solution:

The given system of equations can be written as,

$\frac{xy}{x+y} =\frac{6}{5}$

$5(xy)=6(x+y)$    (On cross multiplication)

$6x+6y=5xy$---(i)

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

$xy=6(y-x)$    (On cross multiplication)

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

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

$6x+6y+6y-6x=5xy+xy$

$12y=6xy$

$\frac{xy}{y}=\frac{12}{2}$

$x=2$

Using $x=2$ in equation (i), we get,

$6(2)+6y=5(2)y$

$12+6y=10y$

$10y-6y=12$

$4y=12$

$y=\frac{12}{4}$

$y=3$

Therefore, the solution of the given system of equations is $x=2$ and $y=3$. 

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Updated on: 10-Oct-2022

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