Pair of Linear ...

Solve: $$3\left ( 2x+y \right )= 7xy$$ and $$3\left ( x+3y \right )= 11xy$$;  

Solve: $$4x+\displaystyle \frac{6}{y}= 15$$ and $$6x-\displaystyle \frac{8}{y}= 14$$. Hence find the value of $$k$$, if $$y= kx-2$$.

If $$1$$ is added to each of the two certain numbers, their ratio is $$1:2$$; and if $$5$$ is subtracted from each of the two numbers, their ratio becomes $$5:11$$. Find the numbers. 

Solve the set of equations: $$3\left ( 2u+v \right )= 7uv$$ and $$3\left ( u+3v \right )= 11uv$$

Solve the following pair of equations :

Solve : $$\displaystyle \frac{9}{x}\, -\, \displaystyle \frac{4}{y}\, =\, 8$$ and $$\displaystyle \frac{13}{x}\, +\, \displaystyle \frac{7}{y}\, =\, 101$$