In the case of a sysadmin job, this is how I would do it: start showing some expertise in configuring Linux virtual instances, discuss why and how you manage them, share tips and tricks you learned. That will do you a lot of good on your resume, help you land interviews, and help you convince during those interviews. Especially if you are competing with other college grads with 0 experience, you'll stand out.

Just imagine a sysadmin turning up with their laptop and demonstrating...

1. Provisioning of servers where they've created the *nix build, deployed a web app, mysql etc

2. They show off their system monitoring capability, take down a few services and then show off their e-mail alerts. Bonus points for twilio integration with SMS :)

3. They then show the backup process they have and how they verify their backups

4. The sysadmin then runs a series of security tests against a server and shows the results

I would hire that guy in an instant