Solve the following pairs of equations by cross-multiplication method:
$3x - 4y = 17$
$4x - 5y = 21$

The sum of the digits of a two-digit number is $9$. The number obtained by interchanging the digits exceeds the original number by $45$. Find the original number.

Draw the graph of the pair of equations $2x + y = 4$ and $2x - y = 4$. Write the vertices of the triangle formed by these lines and the $y$-axis. Also,find the area of this triangle.

$A$ passenger buys $5$ tickets for Ahmadabad to Nadiad and $10$ tickets for Ahmadabad to Vadodara for Rs. $1050$. The total cost of a ticket for Ahmadabad to Nadiad and a ticket for Ahmadabad to Vadodara is Rs. $130$. Find the cost of a ticket for Ahmadabad to Nadiad as well as the cost of a ticket for Ahmadabad to Vadodara.

Prashant purchases $2$ mobiles and $3$ memory cards for Rs. $6500$. The cost of one mobile and one memory card is Rs. $2950$. Represent this as a pair of linear equations in two variables.

The sum of a two-digit number and the number obtained by interchanging its digits is $110$. If the number obtained by subtracting $10$ from the original number exceeds five times the sum of the digits of the original number by $4$,then find the original number.