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

Four years ago,the sum of the ages of a mother and her two daughters was $x$ years. What will be the sum of their ages after two years?

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.

For a pair of equations,if $a_{1} b_{2}-a_{2} b_{1}=0, b_{1} c_{2}-b_{2} c_{1}=0$ and $c_{1} a_{2}-c_{2} a_{1}=0$,then the solution set of the pair of equations is ...........

The ratio of the present ages of Rajan and Jay is $3:2$. After five years,the ratio of their ages will be $4:3$. Find the present ages of both.

If $I$ add $1$ to each of the two given numbers,then their ratio is $1:2$. If $I$ subtract $5$ from each of the numbers,the ratio is $5:11$. Find the numbers.