For a pair of equations $7x - 13y = 1$ and $13x - 7y = 19$,find the value of $x - y$.

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

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 pair of linear equations by the method of substitution: $2x - 3y = -11$ and $4x - 6y + 22 = 0$.

Are the following pair of linear equations consistent? Justify your answer.
$-3x - 4y = 12$
$3x + 4y = 12$

In a two-digit number,the digit at the unit's place is $(x+1)$ and the digit at the ten's place is $(x+2)$,then that number is $\ldots \ldots \ldots \ldots .$