iTunes Match and Apple Music

Hello everybody,

First post here so please bear with me. I have had a quick look on other posts and I do find similarities but please read below.

As I only have 128gb on my MacBook Air and half of that is taken up by music I recently got iTunes Match. The idea was to upload ALL of my music to the cloud and then access and/or download from the cloud on the go. After getting Match I am quite sure that my music has been uploaded (it took quite a while) but I still have all my songs on my hd. So how can I/do I delete my local files while still having access to the music in the cloud? I have Apple Music in my car and can access my entire "My Music" library from there but i fear that won't be the case if I delete my music on my Mac and it's being mirrored to Match. Does any of this make sense?

Thanks in advance.