Ja i moja sestra smo juče bile zajedno u parku.

Because the speakers are two females: ja refers to a female speaker, and moja sestra is also female.

In Serbian past tense, the l-participle agrees in gender and number:

• bio / bila = singular masculine / feminine
• bili / bile = plural masculine or mixed / plural feminine

So:

• Ja i moj brat smo bili... = I and my brother were...
• Ja i moja sestra smo bile... = I and my sister were...

If even one male is included in the group, Serbian normally uses masculine plural: bili.

Serbian past tense is made with two parts:

1. a present-tense form of biti (sam, si, je, smo, ste, su)
2. the l-participle (bio, bila, bili, bile, etc.)

So smo bile literally consists of:

• smo = we are / auxiliary for we
• bile = been / were (feminine plural form)

Together they mean we were.

This is the normal way to form the past tense in Serbian.

Yes, ja could be omitted if the context already makes it clear who is speaking.

Serbian often drops subject pronouns because the verb already gives information about the subject. However, in this sentence, the speaker wants to explicitly say I and my sister, so ja is included.

Compare:

• Ja i moja sestra smo juče bile zajedno u parku. = My sister and I were together in the park yesterday.
• Moja sestra i ja smo juče bile zajedno u parku. = same meaning
• In some contexts, if the speaker has already been established, Serbian might rephrase the sentence rather than simply omit ja, because the subject is a coordinated phrase.

So ja is not required in every sentence, but here it is natural and clear.

Yes, Moja sestra i ja is also correct.

Both are grammatical:

• Ja i moja sestra...
• Moja sestra i ja...

In English, learners are often taught that my sister and I sounds more polite than I and my sister. In Serbian, word order is more flexible, and both versions are common. Sometimes speakers choose the order based on emphasis, rhythm, or personal habit.

So this is mainly a style choice, not a grammar issue.

It is in the nominative, because it is part of the subject of the sentence.

The subject here is:

• ja
• moja sestra

Since both are doing the role of the subject, they stay in nominative:

• moja = feminine singular nominative
• sestra = feminine singular nominative

You are not saying with my sister here. You are saying my sister and I.

If you wanted with my sister, you would use a different structure, for example:

• sa mojom sestrom = with my sister

Yes, juče can move around. Serbian word order is fairly flexible.

This sentence has:

• Ja i moja sestra smo juče bile zajedno u parku.

But these are also possible:

• Ja i moja sestra juče smo bile zajedno u parku.
• Juče smo ja i moja sestra bile zajedno u parku.
• Ja i moja sestra smo bile zajedno u parku juče.

The meaning stays basically the same, but the focus changes slightly.

The version with smo juče bile is natural and neutral.

Zajedno means together.

It is not strictly necessary for grammar, but it adds meaning. Without it:

• Ja i moja sestra smo juče bile u parku. means
• My sister and I were in the park yesterday.

With zajedno:

• Ja i moja sestra smo juče bile zajedno u parku. means
• My sister and I were together in the park yesterday.

So zajedno emphasizes that they were there with each other, not just both there at some point.

Because after u meaning in, Serbian uses the locative case when talking about location.

Here the meaning is in the park, so:

• park → parku (locative singular)

Compare:

• u parku = in the park, at the park location
• u park = into the park, motion toward the inside of the park

So:

• Bile smo u parku. = We were in the park.
• Išle smo u park. = We went to the park.

This is a very important Serbian distinction:

• location → often locative
• destination / motion toward → often accusative

Because Serbian expresses past tense differently from English.

English uses one word:

• were

Serbian usually uses:

• an auxiliary
  • a participle

So were in this sentence is expressed by:

• smo bile

This is completely normal in Serbian:

• Ja sam bila = I was
• Mi smo bile = we were (all female)
• Oni su bili = they were (masculine or mixed group)
• One su bile = they were (female group)

Yes, that is also correct.

In Serbian, the past-tense auxiliary can often appear after the participle in this kind of sentence:

• Ja i moja sestra smo juče bile zajedno u parku.
• Ja i moja sestra bile smo juče zajedno u parku.

Both are grammatical. The first version is probably the more neutral one for many learners to start with.

Serbian clitics like sam, si, smo, ste, su often tend to appear in second position, but real sentence structure can be a bit more flexible than a simple one-rule explanation suggests. At beginner level, it is enough to know that both versions can occur.

Then the participle would become bili, not bile.

So a male speaker would say:

• Ja i moja sestra smo juče bili zajedno u parku.

That may seem surprising at first, because sestra is female. But in Serbian, if a group includes at least one male, the plural agreement is usually masculine.

So:

• female + female → bile
• male + female → bili

Sometimes yes, but usually you would then rephrase the whole subject.

For example, instead of dropping only ja, a speaker might say:

• Moja sestra i ja smo juče bile zajedno u parku.

That often sounds a bit more natural than trying to leave ja out while still keeping the same full meaning.

If the context already makes the speaker obvious, Serbian may also use a different structure entirely, but for learners, the clearest full sentence is exactly the one you have here.

A simple breakdown is:

• Ja i moja sestra = subject
• smo bile = past tense verb phrase
• juče = time expression
• zajedno = adverb
• u parku = place expression

So the full pattern is roughly:

Subject + past tense verb + time + manner/state + place

But remember that Serbian word order is more flexible than English, so these parts can often move around without changing the core meaning.