I don't know what they are called, but i found some good pdf describing them some time ago, now it's lost. I have been searching for "modular systems" but I haven't found anything of worth. Is that their real name or are they called anything else?

An example:

$\displaystyle \left\{\begin{array}{cc}a \cdot x\ +\ b \cdot y\ \equiv\ e\ (\mbox {mod } n) \\

\ c \cdot x\ +\ d \cdot y\ \equiv\ f\ (\mbox {mod } m) \end{array}\right.$

Edit: Oops, I obviously forgot the most important part...

Edit: The next thing to do when I have find a good-looking symetrical solution for this systemis to solve this system:

$\displaystyle \left\{\begin{array}{l}

a_{1,1}\cdot x_1\ +\ a_{1,2}\cdot x_2\ +\ a_{1,3}\cdot x_3\ +\ ...\ a_{1,n}\cdot x_n\ \equiv\ r_1\ (\text{mod }m_1) \\

a_{2,1}\cdot x_1\ +\ a_{2,2}\cdot x_2\ +\ a_{2,3}\cdot x_3\ +\ ...\ a_{2,n}\cdot x_n\ \equiv\ r_2\ (\text{mod }m_2) \\

a_{3,1}\cdot x_1\ +\ a_{3,2}\cdot x_2\ +\ a_{3,3}\cdot x_3\ +\ ...\ a_{3,n}\cdot x_n\ \equiv\ r_3\ (\text{mod }m_3) \\

\vdots \\

a_{n,1}\cdot x_1\ +\ a_{n,2}\cdot x_2\ +\ a_{n,3}\cdot x_3\ +\ ...\ a_{n,n}\cdot x_n\ \equiv\ r_n\ (\text{mod }m_n)

\end{array}\right.$