In a two-digit number, the digit at the unit's place is $(2x - 1)$ and the digit at the ten's place is $(2x + 1)$. Then, that number is:

One says,"Give me a hundred,friend! $I$ shall then become twice as rich as you". The other replies,"If you give me ten,$I$ shall be six times as rich as you". Tell me what is the amount of their (respective) capital?

$x=-1$ and $y=-2$ is one of the solutions of the equation $\ldots \ldots \ldots \ldots$

The cost of $4$ pens and $4$ pencil boxes is $Rs.\, 100$. Three times the cost of a pen is $Rs.\, 15$ more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box (in $Rs.$).

Solve the following pairs of equations:
$\frac{x}{3} + \frac{y}{4} = 4$
$\frac{5x}{6} - \frac{y}{8} = 4$

Solve the following pair of linear equations by the elimination method and the substitution method:
$3x + 4y = 10$ and $2x - 2y = 2$