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If the sum and the difference of the digit at the ten's place and the digit at the unit's place of a two-digit number are the same,then the digit at the unit's place is ...........

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.

If $\frac{x}{2} = \frac{6}{y} = 2$,then the value of $x - y$ is ..........

Solve the following pair of equations by the cross-multiplication method:
$\frac{x}{a} - \frac{y}{b} = 0$
$ax + by = a^2 + b^2$

If zero is inserted between the two digits of a two-digit number whose unit's place is $y$ and ten's place is $x$,then the new number is $\ldots \ldots \ldots \ldots$

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