In a two-digit number, the digit at the unit's place is $(2x - 1)$ and the digit at the ten's place is $(2x + 1)$. Then, that number is:

The solution of a pair of equations $y+x=2$ and $y-x=4$ is $(x, y)=\ldots \ldots \ldots . . .$

In a two-digit number,the digit at the unit's place is $(x+1)$ and the digit at the ten's place is $(x+2)$,then that number is $\ldots \ldots \ldots \ldots .$

The sum of the digits of a two-digit number is $6$. The number obtained by interchanging the digits is $18$ less than the original number. Find the original number.

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

$A$ 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.