Find the values of $x$ and $y$ in the following rectangle.

If $3x + 5y = 8$ and $5x + 3y = 24$,then $x - y = \ldots$

Solve the following pair of linear equations using the cross-multiplication method:
$5x + 2y = 10$
$4x + 3y - 1 = 0$

The equations $\frac{2}{3} x + \frac{3}{2} y = 5$ and $\ldots \ldots \ldots$ are the same.

There are some students in the two examination halls $A$ and $B$. To make the number of students equal in each hall,$10$ students are sent from $A$ to $B$. But if $20$ students are sent from $B$ to $A$,the number of students in $A$ becomes double the number of students in $B$. Find the number of students in the two halls.

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent:
$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$