I seems you have never created a database before otherwise you would never ask such a question. Without system tablespace you cannot have a database in Oracle. A tablespace can belong to only and only one database.

Take a print out of Concepts Guide, take a leave for a week read it throughly. Without knowing the concepts i wonder how you going to backup and recover your PROD database. This is no joke, but a serious advice for you if you want to keep your job as a DBA. And do not forget to read the Backup and Recovery Concepts guide as well.

Download this documentation
http://download.oracle.com/docs/cds/F49540_01.zip
or browse online
http://download-east.oracle.com/docs.../DOC/index.htm

and read them.

HTH