The solution set of a pair of equations $3x + 3y - 3 = 0$ and $5x + 5y - 5 = 0$ is $\ldots \ldots \ldots \ldots$

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent:
$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$

For a pair of equations $7x - 13y = 1$ and $13x - 7y = 19$,find the value of $x - y$.

The length of a rectangle is one and a half times its breadth. If the perimeter of the rectangle is $100 \,cm$, find the length and the breadth of the rectangle.

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:
$(a-b)x + (a+b)y = a^2 - 2ab - b^2$
$(a+b)(x+y) = a^2 + b^2$