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

Devarshi got thrice the marks as obtained by Maharshi in the annual examination of mathematics of standard $10$. The sum of the marks obtained by them was $150$. Represent this situation as a pair of linear equations in two variables.

$A$ passenger buys $5$ tickets for Ahmadabad to Nadiad and $10$ tickets for Ahmadabad to Vadodara for Rs. $1050$. The total cost of a ticket for Ahmadabad to Nadiad and a ticket for Ahmadabad to Vadodara is Rs. $130$. Find the cost of a ticket for Ahmadabad to Nadiad as well as the cost of a ticket for Ahmadabad to Vadodara.

It can take $12$ hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for $4$ hours and the pipe of smaller diameter for $9$ hours,only half the pool can be filled. How long would it take for each pipe to fill the pool separately?

The graph of the equation $\ldots \ldots \ldots \ldots$ is a line perpendicular to the $Y-axis.$

The total cost of $7$ pens and $5$ pencils is Rs. $50$,and the total cost of $5$ pens and $7$ pencils is Rs. $46$. Represent this as a pair of linear equations in two variables.