Solve the pair of linear equations $2x + y = 40$ and $x + y = 30$. If the solution satisfies the equation $y = mx + 6$,find the value of $m$.

$A$ 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 $Rs.$).

If $2x + 3y = 7$ and $3x + 2y = 3$,then the value of $x + y$ is ..........

Do the following pair of linear equations have no solution? Justify your answer.
$y + 6x = 6$ and $y = 2x$

The age of the father is twice the sum of the ages of his two children. After $20$ years,his age will be equal to the sum of the ages of his children. Find the age of the father (in years).

Solve the following pair of linear equations in two variables using the graphical method: $2x + y = 7$ and $x - 2y = 6$.