For the pair of equations $\frac{2}{x} + \frac{3}{y} = 3$ and $\frac{3}{x} + \frac{2}{y} = 7$,find the value of $\frac{3}{x} + \frac{3}{y}$.

Examine graphically whether the pair of equations $2x + 4y = 9$ and $3x + 6y = \frac{27}{2}$ is consistent.

Solve the following pairs of equations by the method of elimination:
$4x - 3y = 5$
$\frac{5}{2}x - y = 4$

For a pair of equations $5x - 4y = 1$ and $10x = 8y + 2$,in usual notations $a_{1}b_{2} - a_{2}b_{1} = \dots$

The solution set of the pair of equations $x = -2$ and $y = 3$ is:

In a two-digit number,the digit at the ten's place is double the digit at the unit's place. If the digits of the number are interchanged,the new number so formed is $27$ less than the original number. Find the original number.