Solve the following pairs of equations by cross-multiplication method:
$3x - 4y = 17$
$4x - 5y = 21$

The standard form of the equation $5y = -2x + 3$ is........

The sum of the digits of a two-digit number is $13$. The number obtained by interchanging the digits is $9$ more than the original number. Find the original number.

The two-digit number whose digit at the unit's place is $x$ and the digit at the ten's place is $y$ is three times the sum of its digits. This statement is written as $\ldots \ldots \ldots \ldots .$

If $\frac{5}{x}+\frac{3}{y}=4$ and $\frac{3}{x}+\frac{5}{y}=2,$ then $\frac{1}{x}-\frac{1}{y}=\ldots \ldots \ldots \ldots .(x, y \neq 0)$

Solve the following pair of linear equations by the method of substitution: $2x + 3y = 7$ and $6x + 9y = 23$.