Solve the following pair of linear equations:
$21x + 47y = 110$
$47x + 21y = 162$

Solve the following pair of equations by the method of cross multiplication:
$x + y - (a + b) = 0$
$ax - by - (a^2 - b^2) = 0$

$x$ years ago,the sum of the ages of a mother,father,and two children was $y$ years. What will be the sum of their ages after $z$ 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.

$A$ number is $3$ less than another number. By adding $17$ to twice the larger number,it becomes thrice the smaller number. Find these numbers.

Comparing the equation $y = -3$ with the standard form $ax + by + c = 0$,we get $a = \dots$