How will we get on? = asking about results. Example: How did Blackpool get on in the Premier league this season? How will we get by? = asking about survival. Example: How will I get by without a job? This is an advanced test. "By" is wrong.

I'm not one for answering people homework but seeing as you have the answer it's alright :) Both "by" and "on" are valid here. They both have the same meaning, that is: "How will we support ourselves?" or "How are we going to pay the bills?" etc.

We don't do homework here. Why don't you try it first?

I think also, you can use both here. 'get on' means to be or to continue . 'get by' means to survive or succeed at a minimal amount of effort or succeed in managing something. Maybe 'get on' is more appropriate to use here ,because there is unemployment ,so there is nothing to manage or effort to exert ,so it is just about continuing to exist and survive the crisis of unempolyment.