What type of situations might be modeled with equations containing two or more variables?

Quite a lot. For example, the equation tracking the path of a ball thrown up in the air as it starts with some velocity and is accelerated downward by gravity.

Many fields have cyclical equations, such as the waveforms of alternating current electricity. Another example is predator-prey cycles in Biology. Predator grows in number, prey is killed off, predator dies from hunger, prey increases in number with less predators, predators grow in number from more food, and so on. Or the rise and fall of a Stock Market.