Examine graphically whether the pair of equations $2x + 4y = 9$ and $3x + 6y = \frac{27}{2}$ is consistent.

Solve the following pairs of equations:
$43x + 67y = -24$
$67x + 43y = 24$

In a two-digit number,the digit at unit's place is $x$ and the digit at ten's place is $y$. The number obtained by interchanging the digits is ...........

Solve the following pairs of equations by the method of elimination:
$\frac{x}{2} + \frac{3y}{5} + 1 = 0$
$\frac{x}{2} + \frac{y}{3} - \frac{1}{3} = 0$

If the lines given by $3x + 2ky = 2$ and $2x + 5y + 1 = 0$ are parallel,then the value of $k$ is

$A$ 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 $Rs.$).