Moja sestra živi u gradu, ali moj brat živi u kući.

Because moj / moja / moje must agree with the gender of the noun.

• sestra is a feminine noun, so you use moja
• brat is a masculine noun, so you use moj

This is the same possessive adjective, just in different forms.

A few basic forms are:

• moj brat = my brother
• moja sestra = my sister
• moje dete = my child

So the ending changes to match the noun.

Serbian normally does not use articles like English the and a/an.

So:

• sestra can mean sister, a sister, or the sister
• brat can mean brother, a brother, or the brother
• grad can mean city, a city, or the city

The exact meaning depends on context. This is very normal in Serbian, so learners have to get used to understanding definiteness without articles.

Because both my sister and my brother are third person singular.

The verb živeti / živjeti means to live. In the present tense:

• ja živim = I live
• ti živiš = you live
• on/ona živi = he/she lives
• mi živimo = we live
• vi živite = you live
• oni/one žive = they live

Both sestra and brat take the he/she lives form, so both use živi.

Because Serbian often leaves subject pronouns out when they are not needed.

English usually says:

• My sister lives...
• My brother lives...

Serbian can also say the subject noun directly without adding ona or on, because the verb form already helps show who the subject is.

So:

• Moja sestra živi...
• Moj brat živi...

sounds completely natural.

If you added ona or on, it would usually be for extra emphasis or contrast, not because grammar requires it.

Because after u meaning in, Serbian uses the locative case.

The noun grad changes in the locative:

• nominative: grad
• locative: gradu

So:

• u gradu = in the city

This is one of the basic case patterns you need to learn: the noun changes form depending on its role in the sentence.

For the same reason: u meaning in takes the locative case.

The noun kuća changes like this:

• nominative: kuća
• locative: kući

So:

• u kući = in the house

This is a feminine noun pattern, while grad is masculine, so the ending changes differently.

Not always. U can mean in or into, depending on the case that follows it.

• u + locative usually means in / inside
• u + accusative usually means into / to

Examples:

• u gradu = in the city
• u kući = in the house
• idem u grad = I am going to the city / into town
• ulazim u kuću = I am entering the house

So in your sentence, u gradu and u kući show location, which is why the locative is used.

Ali means but.

It connects two contrasting ideas:

• Moja sestra živi u gradu
• ali
• moj brat živi u kući

It works very much like English but.

Also, just like in English, a comma before ali is normal here because it joins two full clauses.

No, Serbian word order is more flexible than English word order.

The neutral, natural version is:

• Moja sestra živi u gradu, ali moj brat živi u kući.

But Serbian can move things around for emphasis. For example:

• U gradu živi moja sestra, ali u kući živi moj brat.

That does not change the basic meaning, but it changes what is emphasized.

So the sentence you have is a standard, clear word order, but not the only possible one.

Because Serbian often repeats the subject when it helps make the contrast clear.

In this sentence, the contrast is:

• my sister lives in the city
• but my brother lives in the house

Repeating both noun phrases makes the comparison neat and explicit. You could sometimes shorten things in conversation, but this full version is very natural and good for learners.

Not necessarily. Grad can mean city, but in many contexts it can also mean town.

So u gradu can sometimes feel like:

• in the city
• in town
• downtown / in the urban area

The exact nuance depends on context.

A few sounds here are especially important:

• ž sounds like the s in measure
• ć is a soft sound, somewhat like a very soft ch; English does not have an exact match
• j is pronounced like English y

So roughly:

• živi ≈ ZHEE-vee
• gradu ≈ GRAH-doo
• kući ≈ KOO-chee, but with a softer ch

Also, Serbian spelling is very phonetic, so words are usually pronounced much closer to how they are written than in English.

They are in the nominative case, because they are the subjects of the verbs.

You can see the structure like this:

• Moja sestra = subject
• živi = verb
• u gradu = location

and

• moj brat = subject
• živi = verb
• u kući = location

So the subjects stay in nominative, while the nouns after u change to locative.

Yes, grammatically that is completely correct.

The sentence you were given contrasts two different places:

• u gradu
• u kući

But u kući itself is not tied to brat. You could use either location with either person if the real-life situation is different.

So the grammar pattern is what matters:

• [subject] + živi + u + locative

Examples:

• Moja sestra živi u gradu.
• Moj brat živi u gradu.
• Moja sestra živi u kući.
• Moj brat živi u kući.