Translation:I am travelling with a backpack and a suitcase.
When do you need 'z' and when don't you? In the last sentence it was 'podróżuję pociągiem'?
"Z" means "with" (accompanying) and it is used with Instrumental. It would sound strange if you said "Podróżuję plecakiem i walizką" because it would mean that you are travelling using a backpack and a suitcase in some way, maybe you would ride on them...
- using something
- used to say what fills, covers, etc something
- used to say that people or things are in a place together or are doing something together
- having or including something
- used to describe the way someone does something
This is a dictionary for learning English, so sometimes one English meaning is few different words in Polish (z, o).
In English it is also different to say "I travel by the train" and "I travel with the backpack".
Why "a backpack"? I am traveling with rucksack and suitcase. seems fine but is rejected.
Google says "About 38,000,000 results (0.47 seconds)", there are hundreds of results in British National Corpus and looking at Google NGram shows that it was only 1977, when the use of 'backpack' became more popular than 'rucksack' in English, so this doesn't seem to be entirely true… ;)
Who uses the term 'suitcase'? Personally I travel with a case, maybe a backpack as well. I think I am more likely to say rucksack than I am to say suitcase.
"case" has too many meanings to be the first answer. But it should work, of course. Added now.