После совещания мы сообща решили отложить встречу до пятницы.

Because после requires the genitive case.

• совещание is the dictionary form, nominative singular.
• After после (after), it changes to совещания.

So:

• совещание = a meeting / conference meeting
• после совещания = after the meeting

This is a standard pattern:

• после урока = after the lesson
• после работы = after work
• после обеда = after lunch

These two words can both be translated as meeting, but they are not quite the same.

• совещание usually means a work meeting, staff meeting, or conference/discussion meeting where people discuss something officially.
• встреча is broader. It can mean a meeting, appointment, or get-together.

In this sentence:

• После совещания = after the work meeting
• отложить встречу = postpone the meeting/appointment

So the sentence suggests there was one meeting first, and after that, they decided to postpone another meeting.

Сообща means jointly, together, as a group, or collectively.

So мы сообща решили means something like:

• we decided together
• we all jointly decided

It emphasizes that the decision was made collectively, not by one person.

This word is a little more formal or literary than everyday вместе. In casual speech, many Russians might more naturally say:

• мы вместе решили
• мы все решили

But сообща is completely correct and natural.

Because решили is the past tense plural of the perfective verb решить, and here it means they reached a decision.

• решили = decided, came to a decision
• решали = were deciding / used to decide / spent time deciding

In this sentence, the decision is presented as a completed fact, so решили is the natural choice.

Compare:

• Мы решили отложить встречу. = We decided to postpone the meeting.
• Мы долго решали, что делать. = We spent a long time deciding what to do.

Because отложить is perfective, and after решили it usually expresses a single completed action that they decided to carry out.

• решили отложить = decided to postpone
• решили откладывать would suggest something more repeated, ongoing, or habitual, which does not fit well here

So this pair works naturally:

• решить + perfective infinitive

Examples:

• решили начать = decided to begin
• решили купить = decided to buy
• решили отложить = decided to postpone

Because встречу is the accusative singular form of встреча.

Here, встречу is the direct object of отложить:

• отложить что? → встречу

Since встреча is a feminine noun ending in -а, its accusative singular changes to -у:

• nominative: встреча
• accusative: встречу

The same pattern appears in:

• читать книгу
• видеть сестру
• назначить встречу

До requires the genitive case, so пятница becomes пятницы.

• пятница = Friday
• до пятницы = until Friday / by Friday / as far as Friday

This is another standard pattern:

• до утра = until morning
• до конца недели = until the end of the week
• до понедельника = until Monday

So grammatically, пятницы is genitive singular.

It can suggest postpone it until Friday, and in context that often implies move it to Friday or delay it so it happens no earlier than Friday.

However, if you want to say very clearly reschedule it for Friday, Russian often uses:

• перенести встречу на пятницу = move/reschedule the meeting to Friday

So:

• отложить до пятницы = postpone until Friday
• перенести на пятницу = move to Friday

The sentence you have is natural, but перенести встречу на пятницу would be more precise if the exact new day is important.

Russian word order is flexible, so starting with После совещания puts the time/context first:

• После совещания мы сообща решили отложить встречу до пятницы.

This feels natural if the speaker wants to frame the decision as something that happened after the meeting.

Other word orders are possible, for example:

• Мы после совещания сообща решили отложить встречу до пятницы.

That still means the same thing, but the emphasis shifts slightly. Russian often moves elements around to highlight what is most important in context.

Yes. If you remove сообща, the sentence is still completely grammatical:

• После совещания мы решили отложить встречу до пятницы.

That simply means After the meeting, we decided to postpone the meeting until Friday.

Adding сообща adds emphasis that the decision was made collectively or by everyone together. So it is not necessary for grammar, but it does add a nuance.