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

Write an equation of a line passing through the point representing the solution of the pair of linear equations $x+y=2$ and $2x-y=1$. How many such lines can we find?

$A$ two-digit number is such that the product of its digits is $10$. When $27$ is added to the original number,the new number obtained is the same as the number obtained by interchanging the digits of the original number. Determine the number.

Solve the following pair of equations by the method of cross-multiplication:
$2x + y = 35$
$3x + 4y = 65$

$A$ two-digit number is obtained by either multiplying the sum of the digits by $8$ and adding $1$,or by multiplying the difference of the digits by $13$ and adding $2$. Find the number.

Solve the following pair of linear equations:
$152x - 378y = -74$
$-378x + 152y = -604$