Solve the following system of equations:

$$
\begin{aligned}
& x+y=a \ldots \\
& \frac{1}{x}+\frac{1}{y}=\frac{1}{b} \ldots
\end{aligned}
$$

Determine for what values of $a$ and $b$ the roots are real. What relationship must hold between $a$ and $b$ for one of the roots to be three times the other?