Mac 21 inch made in 2009 OS 10.10.5 yosemite will adobe illustrator 10 work on this computer eve if adobe does not support it

Ask Adobe. It’s their app.

That iMac is well below published requirements:

https://helpx.adobe.com/illustrator/system-requirements.html

Off the top, a quarter of the minimum VRAM, and no Metal support.

So yeah, not likely going to work.

Bob-T Said:

"Mac 21 inch made in 2009 OS 10.10.5 yosemite will adobe illustrator 10 work on this computer eve if adobe does not support it: Ebays sells older software versions there is a copy of Adobe illustrator 10 with serial numbers. Even tho Adobe does not support this would it still work on may above Mac"

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Compatibility is the Culprit:

I don't know if it would work. With such an old Mac, you'd have to verify compatibility. But, beware of scams on eBay. Licensing is a delicate matter, and it is a common scam reported on eBay.