"우리들이 대답해야 돼요."
Translation:We have to reply.
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우리들이 - we
대답하다 - to answer; to reply; to respond
-야 되다/하다 - have to; need to; should (literally "to be becoming only if" since -야 approximates to "only if/when". Note that "to be becoming" is sort of like "to be ok")
-야 attaches to the -아/-어/-여 form of the verb (대답해 in this case)
All together you get "It is ok (돼요) only if (-야) we (우리들이) reply (대답해)", which essentially translates to and means "We have to reply."
Briefly, 야 has several meanings/usages.
But on the 2 specific usages you named:
(1) [V + 아/어/여]-야 하다 / -야 되다 are set patterns indicating a requirement or obligation i.e.
[V + 아/어/여]-야 하다 = have to/must V
[V + 아/어/여]-야 되다 = should V
V = 가(다) = to go
가 + 아-야 하다 = 가야 하다 = must/have got to go
Similarly, 가야 되다 = should go
전 가야 해(요) = I must/have got to go
넌 지금 가야 돼(요) = You should go now
(2) N-(이)야 informal sentence ending [ 해체 (low respect/intimate) ]
(이)야 is/are is the very informal form of 이에요/예요, from 이다(=to be).
It is attached to noun (mostly)/pronoun.
• 너 해고야!
=> 너, as for you + 해고, dismissal (noun) + 야, it is (informal)
= It is dismissal for you
= You are fired!
• 웃지마! 이건 심각한 일이야.
이건 심각한 일이야
=> 이건, This + 심각한, serious + 일, matter (noun) + 이야, is (informal)
= Don't laugh! This is a serious matter.
• 집에 갈 것이야 = 집에 갈 거야 (거 is abbreviation of 것, that)
=> 집에 갈, to be going home + 거, that (pronoun) + 야, it is (informal)
= Lit. (For me) It is that which is to be going home
= I'm going to go home