Solve the following pair of linear equations by the method of substitution: $2x + 3y = 7$ and $6x + 9y = 23$.

The equation $3x - 2y + 5 = 0$ can be written as:

It can take $12$ hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for $4$ hours and the pipe of smaller diameter for $9$ hours,only half the pool can be filled. How long would it take for each pipe to fill the pool separately?

$A$ number is $3$ less than another number. By adding $17$ to twice the larger number,it becomes thrice the smaller number. Find these numbers.

If $2x + y = 23$ and $4x - y = 19$,find the values of $5y - 2x$ and $\frac{y}{x} - 2$.

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