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.

Find the value of $k$ for which the following pair of linear equations has infinitely many solutions:
$kx + 3y = k - 3$
$12x + ky = k$

The solution of the pair of equations $x+2=0$ and $y-1=0$ is $(x, y) = \dots$

The intersection point in the graph of a pair of equations $x=0$ and $y=0$ is.........

$A$ 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.

In a rectangle,the length is $3$ less than twice its width. The perimeter of the rectangle is $100$. Represent this situation as a pair of linear equations in two variables.