Use the method of elimination to find the solution of the following pair of linear equations: $2x + y = 4$ and $x + 3y = 7$.

The graph of the equation $\ldots \ldots \ldots \ldots$ is a line perpendicular to the $X$-axis.

The pair of equations $5x - y = 9$ and $10x - 18 = 2y$ is $\ldots \ldots \ldots \ldots$

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?

In a two-digit number, the digit at the unit's place is $x$ and the digit at the ten's place is $2x$. Then, the number is..........

If the following pair of equations is consistent (unique solution),then find the value of $k$:
$x - ky = 2$
$3x + 2y = -5$