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"operates by" is correct and usable in written English
You can use it to describe how something works, typically in the context of technology or machinery. Example: This machine operates by using a combination of electrical and mechanical components.
Exact(59)
Worse, it operates by consensus.
He operates by impulse.
Kitsch is mechanical and operates by formulas.
Such an alliance operates by the lowest common denominator.
Mother Nature operates by her own iron laws.
But the EU also operates by peer pressure.
It operates by the rules and rhythms of David Bouley.
operates by consensus, any member can veto an agreement.
It operates by dividing the whole into disconnected parts.
The forum, still largely informal, operates by consensus and peer pressure, not sanctions and rules.
Thompson operates by the philosophy he learned as an apprentice under Wolf.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com