If the sum and the difference of the digit at the ten's place and the digit at the unit's place of a two-digit number are the same,then the digit at the unit's place is ...........

If $y = \frac{1}{2} x$ and $x + 2y = 8$,then $x = \dots$

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:

For a pair of equations,if $a_{1} b_{2}-a_{2} b_{1}=0, b_{1} c_{2}-b_{2} c_{1}=0$ and $c_{1} a_{2}-c_{2} a_{1}=0$,then the solution set of the pair of equations is ...........

Solve the following pairs of equations by the method of elimination:
$5(x-2) + 3y = 1$
$3(x+1) + 5(y-3) = 1$

If in a rectangle,the length is increased and breadth reduced each by $2$ units,the area is reduced by $28$ square units. If,however,the length is reduced by $1$ unit and the breadth increased by $2$ units,the area increases by $33$ square units. Find the area of the rectangle.