The sum of the digits of a two-digit number is $9$ and the difference is $1$. The number is ............

Determine,graphically,the vertices of the triangle formed by the lines $y=x$,$3y=x$,and $x+y=8$.

For a two-digit number,if the sum of its digits is equal to the product of its digits,then the number is .............

Solve the pair of linear equations $2x + y = 40$ and $x + y = 30$. If the solution satisfies the equation $y = mx + 6$,find the value of $m$.

The solution set of the pair of equations $2x + 3y = 4$ and $6x + 9y = 17$ is ............

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.