If $\frac{3}{x}-\frac{2}{y}=5$ and $\frac{4}{x}-\frac{5}{y}=2,$ then the value of $\frac{1}{x}-\frac{1}{y}$ is ............ $(x, y \neq 0)$

Form the pair of linear equations in the following problems,and find their solutions (if they exist) by the elimination method.
Meena went to a bank to withdraw ₹ $2000$. She asked the cashier to give her ₹ $50$ and ₹ $100$ notes only. Meena got $25$ notes in all. Find how many notes of ₹ $50$ and ₹ $100$ she received.

Solve the following pairs of equations by the method of elimination:
$5(x-2) + 3y = 1$
$3(x+1) + 5(y-3) = 1$

Solve the following pairs of equations:
$4x + \frac{6}{y} = 15$
$6x - \frac{8}{y} = 14, y \neq 0$

Form the pair of linear equations for the following problem,and find their solutions (if they exist) by the elimination method:
If we add $1$ to the numerator and subtract $1$ from the denominator,a fraction reduces to $1$. It becomes $\frac{1}{2}$ if we only add $1$ to the denominator. What is the fraction?

Obtain the solution of the following pair of equations by elimination method:
$\frac{11}{y} - \frac{7}{x} = 1, \, \frac{9}{y} - \frac{4}{x} = 6$; $x \neq 0, \, y \neq 0$