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

The solution set of $2x + 3y = 5$ and $4x + ky = 10$ is an infinite set. The value of $k$ is ...........

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.

If $\frac{x+y}{x y}=2$ and $\frac{x-y}{x y}=6,$ then $x=\ldots \ldots \ldots \ldots .$

The solution of the pair of equations $x + 2y = 5$ and $2x + y = 4$ is .........

Solve the following pair of linear equations: $\frac{8}{a} - \frac{9}{b} = 1$ and $\frac{10}{a} + \frac{6}{b} = 7$.