For the linear equation of two variables $ax + by + c = 0$,$\ldots \ldots \ldots \ldots$ is not true.

Find the value of $k$ for which the following pair of linear equations has infinitely many solutions:
$kx + 3y = k - 3$
$12x + ky = k$

While arranging the students of standard $X$ in rows,if two rows are reduced,then one more student has to be arranged in each of the remaining rows. If three more rows are formed,then one student has to be taken off from each of the previously arranged rows. Find the total number of students in the class.

$A$ shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days,and an additional charge for each day thereafter. Latika paid $Rs. 22$ for a book kept for six days,while Anand paid $Rs. 16$ for the book kept for four days. Find the fixed charges and the charge for each extra day (in $Rs.$).

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

Solve the following pair of equations by the method of cross-multiplication:
$x + 2y + 1 = 0$
$2x - 3y - 12 = 0$