If $5x + 3y = 10xy$ $(x \neq 0, y \neq 0)$,then $\frac{6}{x} + \frac{10}{y} = ...........$

Do the following pair of linear equations have no solution? Justify your answer.
$y + 6x = 6$ and $y = 2x$

For which values of $a$ and $b$ does the following pair of linear equations have infinitely many solutions?
$x + 2y = 1$
$(a - b)x + (a + b)y = a + b - 2$

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

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.

Solve the following pair of linear equations: $x+y=5xy$ and $3x+2y=13xy$.