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The phrase "accepted system" is correct and usable in written English.
It can be used to refer to a system that is widely recognized or approved within a particular context or field.
Example: "The accepted system for measuring temperature in scientific research is the Celsius scale."
Alternatives: "recognized system" or "established system".
Exact(35)
"Unfortunately, getting ahead of others is part of the accepted system", he says.
Aircraft installations are less common than those of VOR/DME, the internationally accepted system for position finding.
A variety of histologic grading systems for ovarian carcinoma have been used, but there is no widely accepted system.
Presently, several products are used, but no universally accepted system is promoted because very disparate limitations exist.
Before leaving the bank in 1909, Lamont went to Europe for the American Bankers Association to establish an internationally accepted system of drafts known as travelers' checks.
This classification was later adopted and expanded by Erich von Hornbostel and Curt Sachs and has become the most commonly accepted system of instrument classification.
Similar(25)
Bio-inspired synthesis of ZnO nanoparticles has been achieved using environmentally and eco-friendly accepted systems.
Teeth and their relative structures (apical and periodontal tissues): Teeth can be numbered using three internationally accepted systems.
Accepting System of Rice Intensification (SRI) by farmers in rainfed lowland paddy area of Cambodia.
The typical learning target is pointers, for which teachers tend not to accept system's visualizations.
You have omitted the hyphen once… What do you wish to do? (Options: accept system's decision; system justify itself, accept compromise (2), justify myself…).
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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