If $2x + y = 23$ and $4x - y = 19$,find the values of $5y - 2x$ and $\frac{y}{x} - 2$.

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.

The sum of the digits of a two-digit number is $13$. The number obtained by interchanging the digits is $9$ more than the original number. Find the original number.

For what value of $k,$ do the equations $3x - y + 8 = 0$ and $6x - ky = -16$ represent coincident lines?

If $3x + 5y = 8$ and $5x + 3y = 24$,then $x - y = \ldots$

Students of a class are made to stand in rows. If $1$ student is extra in a row,there would be $2$ rows less. If $1$ student is less in a row,there would be $3$ rows more. Find the total number of students in the class.