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Solve the following pair of linear equations: $\frac{9}{a} + \frac{8}{b} = 7$ and $\frac{2}{a} - \frac{3}{b} = -8$.

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

Solve the following pairs of linear equations: $\frac{5}{a} - \frac{6}{b} = 3$ and $\frac{1}{a} + \frac{4}{b} = 11$.

Solve the following pairs of linear equations: $\frac{2}{x} + \frac{3}{y} = \frac{9}{xy}, \quad \frac{4}{x} + \frac{9}{y} = \frac{21}{xy} \quad (x \neq 0, y \neq 0)$

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$A$ two-digit number is obtained by either multiplying the sum of the digits by $8$ and adding $1$,or by multiplying the difference of the digits by $13$ and adding $2$. Find the number.

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