If the pair of equations $\frac{5}{x} - \frac{3}{y} = 9$ and $\frac{3}{x} - \frac{5}{y} = 7$,then $\frac{1}{x} - \frac{1}{y} = \ldots$

Solve the following pair of equations: $(a \neq 0, b \neq 0)$
$\frac{2}{a} + \frac{3}{b} = 1$
$\frac{1}{a} + \frac{1}{b} = 1$

Are the following pair of linear equations consistent? Justify your answer.
$-3x - 4y = 12$
$3x + 4y = 12$

Draw the graphs of the equations $x=3, x=5$ and $2x-y-4=0$. Also,find the area of the quadrilateral formed by these lines and the $x$-axis.

The sum of the digits of a two-digit number is $13$. The number obtained by interchanging the digits is $9$ more than the original number. Find the original number.

The total cost of $3 \,kg$ of mangoes and $1 \,kg$ of pomegranate is Rs. $200$,and the total cost of $1 \,kg$ of mango and $1 \,kg$ of pomegranate is Rs. $80$. Represent this situation as a pair of linear equations in two variables.