Without knowing what that third-party system is, it is hard to give a good reccomendation here.
One approach is using Marketo Forms 2.0 as usual, and then write some custom JavaScript on form submit to also send this data to the other system.
A different approach would to be using a webhook. Use Forms 2.0 as usual, using a webhook Marketo can inform the third-party system that the form was filled.
http://developers.marketo.com/documentation/webhooks/