Question

Solve the following systems of equations:

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

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

Answer 1

The given system of equation is

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

=> 5xy = 6(x + y)

=> 5xy = 6x + 6y ....(i)

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

=> xy = 6(y -x)

=> xy= 6y - 6x ....(ii)

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

 6xy = 6y + 6y

=> 6xy = 12y

${\displaystyle \Rightarrow x=\frac{12y}{6y}=2}$

Putting x = 2 in equation (i), we get

${\displaystyle 5\times 1\times y=6\times 2+6y}$

=> 10y =  12 + 6y

=> 10y - 6y = 12

=> 4y = 12

${\displaystyle \Rightarrow y=\frac{12}{4}=3}$

Hence, solution of the given system of equation is x = 2, y =3