Solve the following pair of equations by the cross-multiplication method:
$\frac{x}{5} - \frac{y}{4} = \frac{9}{40}$
$\frac{x}{3} - \frac{y}{2} = \frac{5}{12}$

The total cost of $7$ pens and $5$ pencils is Rs. $50$,and the total cost of $5$ pens and $7$ pencils is Rs. $46$. Represent this as a pair of linear equations in two variables.

Two straight paths are represented by the equations $x-3y=2$ and $-2x+6y=5$. Check whether the paths cross each other or not.

The digit at the ten's place is $4$ in a two-digit number,and the product of both the digits is four times greater than the digit at the ten's place. Find the number.

$A$ shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days,and an additional charge for each day thereafter. Latika paid $Rs. 22$ for a book kept for six days,while Anand paid $Rs. 16$ for the book kept for four days. Find the fixed charges and the charge for each extra day (in $Rs.$).

Solve the following pair of linear equations in two variables graphically: $2x + 3y = 12$ and $2x + 3y = 6$.