get by without doing something
to get away with
Structure
- Verb[ ず ] + に済む
- Verb[ なくて ] + に済む
- Verb[ ないで ] + に済む
This doesn’t seem to currently accept any ないですむ conjugation as a correct response. In addition, the grammar point is listed as ないでにすむ instead of ないですむ. This goes against what is written An Integrated Approach to Intermediate Japanese (the textbook I read) as well as other linked “additional reading.” I’ve not encountered なくてすむ yet, but it seems that it’s structured the same way. It would also be nice to know which forms are used more in writing and which are used more in speech. Thanks in advance!
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Hey 
You are absolutely right!
I have fixed the structure section, and now alternative answers (なくて・ないで) are all accepted.
When it comes to speech or writing, I would say that the expression that is most likely to be seen is ずに済む. Though it is not really restricted to writing or anything like that, since you can hear it in daily conversations, I would even say that much more often than ないで済む and なくて済む。
I would say:
Formality:
ずに済む=>(the same, or minimally more, thanks to ず sounds a bit oldfashioned)なくて済む＝ないで済む
Frequency (how often it is used):
ずに済む (especially せずに済む)>なくて済む>ないで済む
Cheers,
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