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

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.

By the method of substitution,solve the following pair of linear equations: $3x - 7y = 18, 6x - 14y = 12$.

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.

In the pair of equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,if ............ then it has a unique solution.

.......... is not a linear equation of two variables.