The sum of two numbers is $8$. If the smaller number is $y$,then the larger number $x = \ldots \ldots \ldots \ldots$

The sum of two positive numbers is $25$. Five times the smaller number is $5$ more than three times the larger number. Represent this as a pair of linear equations in two variables.

$A$ two-digit number is obtained by either multiplying the sum of the digits by $8$ and then subtracting $5$,or by multiplying the difference of the digits by $16$ and then adding $3$. Find the number.

The sum of a two-digit number and the number obtained by interchanging its digits is $110$. If the number obtained by subtracting $10$ from the original number exceeds five times the sum of the digits of the original number by $4$,then find the original number.

Find the value of $k$ for the following pair of linear equations such that the system has no solution:
$2x - ky + 3 = 0$
$3x + 2y - 1 = 0$

For which values of $p$ and $q$ will the following pair of linear equations have infinitely many solutions?
$4x + 5y = 2$
$(2p + 7q)x + (p + 8q)y = 2q - p + 1$