ずに済む means "get by without doing": something you expected to have to do – a cost, a chore, something unpleasant – turned out to be unnecessary. Take the ない-form and replace ない with ずに済む: 払わない gives . conjugates like any う-verb, and you meet it most as or , reporting something you were spared.
、。
I had an umbrella, so I didn't get wet.
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I got by without a taxi, so I saved money.
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I had insurance, so I didn't have to pay for expensive repairs.
becomes せずに済む, and
becomes
, read こずに済む.
、。
Thanks to the medicine, I didn't need surgery.
In the non-past, ずに済む says what you could be spared, often with or in a question.
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I might not have to work overtime this time.
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Isn't there some way to avoid having to move?
ずに済む, ないで済む and なくて済む
and
mean the same. ずに済む is the most formal of the three and the usual one in writing; in conversation ないで済む and なくて済む are more common.
、。
If I can get away without apologizing, I'd like to.