A system is a method, a way of doing things, a structure, or a form of organization:
I have a system in place for organizing paperwork.
Our company has a unique system of accounting.
Have you ever used the highway transportation system in the United States?
A sprinkler system keeps a lawn watered on a regular basis.
Your body’s respiratory system takes in oxygen and expels carbon dioxide.
The political system in the United States is dominated by Democrats and Republicans.
Some acidic food does not agree with my system. (This is what you might hear a person say when talking about food or drink that causes digestive problems.)
The solar system is the collection of planets that orbit the sun.
solar system
In some cases the word "system" is used when expressing unhappiness or criticism of established norms in society:
You can’t beat the system.
Don’t let the system get you down.
We’re all at the mercy of the system.
Protestors gathered to voice their opposition to the system.
The word "systematic" is an adjective:
Rodney takes a systematic approach to everything that he does.
A systematic review of work completed helps to improve quality at our company.
Continuous improvement is systematically embedded within our organization. (The word "systematically" is an adverb.)
solar system