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.

Solve the following pair of linear equations in two variables using a graph: $x + y = 8$ and $x - y = 2$.

If $y = \frac{1}{2} x$ and $x + 2y = 8$,then $x = \dots$

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.

For the pair of equations $\frac{2}{x} + \frac{3}{y} = 3$ and $\frac{3}{x} + \frac{2}{y} = 7$,find the value of $\frac{3}{x} + \frac{3}{y}$.

For a pair of equations $\frac{2}{x} + \frac{3}{y} = 17$ and $\frac{3}{x} + \frac{2}{y} = 13$,find the value of $\frac{1}{x} + \frac{1}{y}$.