$x=-1$ and $y=-2$ is one of the solutions of the equation $\ldots \ldots \ldots \ldots$

In the pair of linear equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,if $\ldots \ldots \ldots \ldots$,then the system has infinitely many solutions.

Solve the following pair of equations by the method of cross multiplication:
$ax + by - a + b = 0$
$bx - ay - a - b = 0$

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.

The solution set of $2x + 3y = 5$ and $4x + ky = 10$ is an infinite set. The value of $k$ is ...........

Obtain the solution of the following pair of equations by the cross-multiplication method: $ax + by = 1$ and $bx + ay = \frac{2ab}{a^2 + b^2}$.