Solve the following pairs of linear equations: $\frac{5}{a} - \frac{6}{b} = 3$ and $\frac{1}{a} + \frac{4}{b} = 11$.

Which of the following groups truly matches the data of Part $I$ with the data of Part $II$?

Part $I$	Part $II$
$1.$ The solution of $2x - y = 4$ and $3x - 2y = 5$	$a.$ $x = 3, y = 2$
$2.$ The solution of $5x - y = 14$ and $4x - 3y = 9$	$b.$ $x = 3, y = 1$
$3.$ The solution of $4x - 3y = 5$ and $3x - y = 5$	$c.$ $x = 2, y = 1$
$4.$ The solution of $3x - 2y = -1$ and $2x - 5y = -8$	$d.$ $x = 1, y = 2$

For a pair of equations $7x - 13y = 1$ and $13x - 7y = 19$,find the value of $x - y$.

Two years ago,Salim was thrice as old as his daughter and six years later,he will be four years older than twice her age. How old are they now? (in $year$)

$x$ is larger in two numbers $x$ and $y$. Two times the larger number is $4$ more than five times the smaller number. The equation form of this data is $\ldots \ldots \ldots \ldots$

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.