The sum of the digits of a two-digit number is $9$ and the difference is $1$. The number is ............

Find the value of $k$ under the given condition for the following pair of linear equations: $2x - 3y = 1$ and $kx + 5y = 7$,such that the system has a unique solution.

Which of the following pairs of linear equations has a unique solution,no solution,or infinitely many solutions? In case there is a unique solution,find it by using the cross-multiplication method.
$2x + y = 5$
$3x + 2y = 8$

For which values of $a$ and $b$ does the following pair of linear equations have infinitely many solutions?
$x + 2y = 1$
$(a - b)x + (a + b)y = a + b - 2$

The length of a rectangle is five less than thrice its breadth. The perimeter of a rectangle is $110$. If we take $l$ as length and $b$ as breadth,then which of the following equations represents the relationship between length and breadth?

Two numbers are in the ratio $5:6$. If $8$ is subtracted from each of the numbers,the ratio becomes $4:5$. Find the numbers.