For a pair of equations $\frac{2}{x} + \frac{3}{y} = 17$ and $\frac{3}{x} + \frac{2}{y} = 13$,find the value of $\frac{1}{x} + \frac{1}{y}$.

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.

It can take $12$ hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for $4$ hours and the pipe of smaller diameter for $9$ hours,only half the pool can be filled. How long would it take for each pipe to fill the pool separately?

Solve the following pair of equations: $2x + y = \frac{7xy}{3}, x + 3y = \frac{11xy}{3}$

Graphically,solve the following pair of equations:
$2x + y = 6$
$2x - y + 2 = 0$
Find the ratio of the areas of the two triangles formed by the lines representing these equations with the $x$-axis and the lines with the $y$-axis.

The solution set of a pair of equations $x=4$ and $y=5$ is $\ldots \ldots \ldots \ldots$