In what way is the mixed market economy of the united states a democratic system

It is a democratic system because it helps both companies and people. 

It helps companies through the system of the free market and free trade which makes the economy democratic. Any person can open a company and join the market regardless of their background and nobody can kick someone out or forbid them from participating in the market unless they break a law or anything similar.

The way it is democratic for the people is that the government can sometimes intervene in order to protect people from malpractices. This can either be things like monopolies and trusts or it can be social issues like banning segregation in companies and service providing facilities, or for example making an act that raises the minimum wage or anything similar.