Use a momentary to seal and un-seal a circuit

Still a bit new with relay logics.

I have been asked to use one push button to start and stop the system. I have used the PB to create a seal-in circuit to hold the system in the ON state, but my question is, how can I use the same PB to break the system ON state?

You need a toggle function.
You should be able to do this with one-shot contacts.

Having said that I don't think anyone would recommend Starting & Stopping with just one bit unless it's from a selector switch
e.g. 1 = Run, 0 = Stop

Roy

Agree with Roy. I personally would never use this in a real application, but if you do a seach on the site for "toggle" or "flip flop" I believe you will find numerous examples of how to accompolish this on many different platforms.

While it is a good exercise to teach relay logic and in the field may be OK for non critical non hazardous stuff
I stil prefer the green start and the red stop buttons.

There are several good examples here in the website - use the search for flip flop.
Dan Bentler

Yup! It never stops. The human desire for knowledge.

this sounds like a student assignment - right? ... no problem with that - but the objective of the assignment is NOT to just "get it to work" ... the real objective is (or at least SHOULD BE) to teach you some important facts about how the PLC processor executes ("scans") its ladder logic program ...

so ...

even if you just find the "answer" by doing a forum search, be SURE that you "think through" how the various program instructions are functioning FOR AT LEAST THREE OR FOUR passes ("scans") through the program ... there are some important "nuts and bolts" lessons to be learned here - but unfortunately many (most?) students miss them ...

good luck with your project ...