‘with’ or ‘by’ case studies

I have the following sentence:

“Section 4 demonstrates the benefits of the developed methods with three case studies”

Is ‘with’ correct here? Or do I have to use ‘by’?

I’d appreciate every comment.

Answer

Use by instead of with….

We use by when we say what we do to get a result. 
See:
https://dictionary.cambridge.org/grammar/british-grammar/prepositions-and-particles/by

So ” Section 4 demonstrates the benefits of the developed methods by three case studies”

Attribution
Source : Link , Question Author : PeterBe , Answer Author : Alka Yadav

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