How do I find out effectively what particular formal system I'm using in any particular moment when doing math in school?

Question

I would like to know: How to find out in what particular formal system I am working (what axioms, rules of inference and formal language am I assuming) when they don't specify me in a school? For example, in what particular formal system in mathematics are located the following statements?:

1) 4+5=9

2) 2x-1=7