eke out vs supplement

eke out is not a noun while supplement is a noun.

Word	Noun	Adjective	Verb	Adverb
eke out	No	No	Yes	No
supplement	Yes	No	Yes	No

As verbs, supplement is a hypernym of eke out; that is, supplement is a word with a broader meaning than eke out:

eke out (noun)	supplement (noun)
	a supplementary component that improves capability
	a quantity added (e.g. to make up for a deficiency)
	textual matter that is added onto a publication; usually at the end

eke out (verb)	supplement (verb)
obtain with difficulty	add to the very end
make by laborious and precarious means	add as a supplement to what seems insufficient
supplement what is thought to be deficient	serve as a supplement to
live from day to day, as with some hardship