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

Write an equation of a line passing through the point representing the solution of the pair of linear equations $x+y=2$ and $2x-y=1$. How many such lines can we find?

If $x=a$ and $y=b$ is the solution of the equations $x-y=2$ and $x+y=4,$ then the values of $a$ and $b$ are,respectively:

The standard form of $2x = 5y$ is............

The sum of a two-digit number and the number obtained by interchanging its digits is $110$. If the number obtained by subtracting $10$ from the original number exceeds five times the sum of the digits of the original number by $4$,then find the original number.

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.