The sum of a two-digit number and the number obtained by interchanging the digits is always divisible by $\ldots \ldots \ldots \ldots$

The solution set of $2x + 3y + 5 = 0$ and $4x + 6y + 10 = 0$ is........

$A$ shopkeeper sells $4$ pants and $3$ shirts for Rs. $5000$. The cost of a pair of a pant and a shirt is Rs. $750$. Represent this situation as a pair of linear equations in two variables.

The cost of $4$ pens and $4$ pencil boxes is $Rs.\, 100$. Three times the cost of a pen is $Rs.\, 15$ more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box (in $Rs.$).

Solve the following pair of equations: $2x + y = \frac{7xy}{3}, x + 3y = \frac{11xy}{3}$

Which of the following is a linear equation in two variables?