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From the above we can say that the FED and the Treasury department, who must be independent of each other, are an inflation machine.
The FED issues the money that the Treasury must use, when the Treasury does not have enough to pay the debt with the FED, it puts Treasury Bonds on sale, which are sometimes purchased by the FED with money that they print in their machines.
On the other hand, when there is no production or there is a financial crisis, more money is printed and given away, which further inflates the economy with injected money.
In short, they are neither separate nor counterpart, they work together.
I lend you, you have nothing to pay with, sell any rubbish that I buy from you so that you have more money, which I give you myself, with whom you have the debt, but if your business is bad, let me know that I will give you more money to that you can solve. The never ending story.
I have a doubt:
The Federal Reserve Banks, in what sense are they Banks? They are Reserve of what? And if they are private, why do they say they are Federal?