Find the value$(s)$ of $p$ for the pair of equations $2x + 3y - 5 = 0$ and $px - 6y - 8 = 0$ if the system has a unique solution.

$A$ number is $3$ less than another number. By adding $17$ to twice the larger number,it becomes thrice the smaller number. Find these numbers.

Kushan went to a bookseller's shop and purchased $2$ textbooks of Mathematics $IX$ and $3$ textbooks of Mathematics $X$ for Rs. $250$. His friend Rajan also bought $4$ textbooks of Mathematics $IX$ and $6$ textbooks of Mathematics $X$ of the same kind for Rs. $500$. Represent this situation as a pair of linear equations in two variables.

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.

The graph of the equation $\ldots \ldots \ldots \ldots$ is parallel to the $Y$-axis.

The cost of $4$ pens and $4$ pencil boxes is $Rs.\, 100$. Three times the cost of a pen is $Rs.\, 15$ more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box (in $Rs.$).