Solve the following pair of linear equations by the method of substitution: $5x - 3y = 1$ and $2x + 5y = 19$.

$A$ 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 pairs of equations:
$\frac{1}{2x} - \frac{1}{y} = -1$
$\frac{1}{x} + \frac{1}{2y} = 8, \quad x, y \neq 0$

Do the following pair of linear equations have no solution? Justify your answer.
$2x + 4y = 3$
$x = 2y$

Solve the following pair of equations by the cross-multiplication method:
$\frac{x}{a} - \frac{y}{b} = 0$
$ax + by = a^2 + b^2$

The equation of a line which is parallel to the line $x+3y=5$ is $\ldots \ldots \ldots \ldots$