Form the pair of linear equation in the following problem, and find their solutions (if they exist) by the elimination method:

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Form the pair of linear equation in the following problem, and find its solution (if it exists) by the elimination method:

The sum of the digits of a two-digit number is $9.$ Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

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 $\mathrm{₹}2000$. She asked the cashier to give her $\mathrm{₹}50$ and $\mathrm{₹}100$ notes only. Meena got $25$ notes in all. Find how many notes of $\mathrm{₹}50$and $\mathrm{₹}100$ she received.

Form the pair of linear equations in the following problem, and find its solution (if they exist) by the elimination method:

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid $₹27$for a book kept for seven days, while Susy paid $₹21$for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Check whether the following pair of linear equation has a unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method.

$2x+y=5 , 3x+2y=8$

Check whether the following pair of linear equation has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method.

$3x-5y=20 , 6x-10y=40$

Does the following pair of linear equation have a unique solution, no solution, or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.

$x-3y-7=0$ , $3x-3y-15=0$