In a two-digit number,the digit at the unit's place is $3x$ and the digit at the ten's place is $2x$. Then,that number is $\ldots \ldots \ldots \ldots$

The length of a rectangle is five less than thrice its breadth. The perimeter of a rectangle is $110$. If we take $l$ as length and $b$ as breadth,then which of the following equations represents the relationship between length and breadth?

Solve the following pairs of equations by the cross-multiplication method:
$4x + 6y = 11$
$5x - 8y = 6$

Solve the following pair of equations by the method of cross-multiplication:
$x + 2y + 1 = 0$
$2x - 3y - 12 = 0$

Solve the following pairs of equations by the cross-multiplication method:
$x - 3y = -5$
$3x = 7y - 13$

If the following pair of equations has infinite solutions,then find the value of $k$:
$5x + 2y = k$
$10x + 4y = 3$