In a two-digit number, the digit at the unit's place is $x$ and the digit at the ten's place is $2x$. Then, the number is..........

The solution set of $2x + 3y + 5 = 0$ and $4x + 6y + 10 = 0$ is........

If $\frac{3}{x}-\frac{2}{y}=5$ and $\frac{4}{x}-\frac{5}{y}=2,$ then the value of $\frac{1}{x}-\frac{1}{y}$ is ............ $(x, y \neq 0)$

$A$ mother tells her son,"Five years ago,$I$ was five times as old as you were. After ten years,$I$ will be two times as old as you will be." Represent this situation as a pair of linear equations in two variables.

Solve the following pair of linear equations in two variables using the graphical method: $2x + y = 7$ and $x - 2y = 6$.

Solve the following pair of linear equations:
$\frac{x}{a} + \frac{y}{b} = a + b$
$\frac{x}{a^{2}} + \frac{y}{b^{2}} = 2, \quad a, b \neq 0$