Cross the country OR Across the country... question?

Those make me always confused...

How to say implemented systems cross Europe or across Europe?

Hi,

I'm not a teacher, but this is my take on,

It should be 'across Europe' as a preposition.

When natives pronounce the word, it sounds 'cross'

For example:

...implemented systems across Europe.

...installed systems on over 300 branches across the country.

...conducting projects across Europe.

...travelling across Europe.

Are those corrects?

Yes, they are all correct.:-)