For a pair of equations $13x - 7y = 19$ and $7x - 13y = 31$,find the value of $x + y$.

Subtraction of two numbers is $5$. If the larger number is $x$,then the smaller number is $y = \ldots \ldots \ldots \ldots$

Solve the following pair of linear equations:
$x + y = 3.3$
$\frac{0.6}{3x - 2y} = -1$,where $3x - 2y \neq 0$

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

Part $I$	Part $II$
$1. x+2y=3, 2x+4y=5$	$a. \text{Solution set is a singleton set.}$
$2. 2x+3y=6, x+\frac{3}{2}y=3$	$b. \text{Solution set is an empty set.}$
$3. 3x-y=0, x-y+6=0$	$c. \text{Solution set is an infinite set.}$
	$d. \text{Solution set contains two members.}$

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method.
Yash scored $40$ marks in a test,getting $3$ marks for each right answer and losing $1$ mark for each wrong answer. Had $4$ marks been awarded for each correct answer and $2$ marks been deducted for each incorrect answer,then Yash would have scored $50$ marks. How many questions were there in the test?

The sum of the digits of a two-digit number is $9$. The number obtained by interchanging the digits exceeds the original number by $45$. Find the original number.