Find the value$(s)$ of $p$ for the equations $-3x + 5y = 7$ and $2px - 3y = 1$ if the lines represented by these equations intersect at a unique point.

$A$ railway half ticket costs half the full fare,but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from station $A$ to $B$ costs $Rs. 2530$. Also,one reserved first class ticket and one reserved first class half ticket from $A$ to $B$ costs $Rs. 3810$. Find the full first class fare from station $A$ to $B$,and also the reservation charges for a ticket (in $Rs.$).

Solve the following pair of equations: $(a \neq 0, b \neq 0)$
$\frac{2}{a} = -1 - \frac{3}{b}$
$\frac{9}{b} = \frac{4}{a} + 7$

The general form of a linear equation in two variables is .......... (where,$a^{2}+b^{2} \neq 0$).

If $\frac{5}{x}-\frac{4}{y}=4$ and $\frac{4}{x}-\frac{5}{y}=5,$ then $\frac{1}{x}-\frac{1}{y}=\ldots \ldots \ldots \ldots .(x, y \neq 0)$

Places $A$ and $B$ are $90\, km$ apart from each other on a highway. $A$ car starts from $A$ and another from $B$ at the same time. If they move in the same direction,they meet in $9$ hours and if they move in opposite directions,they meet in $\frac{9}{7}$ hours. Find the speeds of the cars.