In a two-digit number, the digit at the unit's place is $(2x - 1)$ and the digit at the ten's place is $(2x + 1)$. Then, that number is:

Solve the following pairs of equations by the method of elimination:
$9x + 7y = 55$
$7x + 9y = 57$

Aruna has only $Rs. 1$ and $Rs. 2$ coins with her. If the total number of coins that she has is $50$ and the amount of money with her is $Rs. 75$,then the number of $Rs. 1$ and $Rs. 2$ coins are,respectively

Solve the following pairs of equations by cross-multiplication method:
$3x + y = 5$
$5x + 3y = 3$

Solve the following pair of linear equations by the method of substitution: $x + 11y = 1$ and $8x + 13y = 2$.

Solve the following pair of equations by the cross-multiplication method:
$ax - by = \frac{a-b}{2}$
$x + 3y = 2$