Solve the following pairs of equations by the cross-multiplication method:
$4x - 19y + 13 = 0$
$13x - 23y + 19 = 0$

The sum and difference of the reciprocals of the ages of a son and father are respectively $\frac{5}{40}$ and $\frac{3}{40}$. Represent this as a pair of linear equations in two variables,where $x$ is the age of the son and $y$ is the age of the father.

In a competitive examination,one mark is awarded for each correct answer while $\frac{1}{2}$ mark is deducted for every wrong answer. Jayanti answered $120$ questions and got $90$ marks. How many questions did she answer correctly?

The equations $\frac{2}{3} x + \frac{3}{2} y = 5$ and $\ldots \ldots \ldots$ are the same.

The pair of equations $5x - y = 9$ and $10x - 18 = 2y$ is $\ldots \ldots \ldots \ldots$

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?