How to delete songs on an iphone 5s?

So i want to get rid of songs. I do the thing where you slide the song from right to left (not left to right) and press the delete button but the songs always come back. How do i get rid of it on my iphone 5s or macbook pro

Here are the steps to delete Songs From iPhone 5s:
From the Settings control panel, tap "iTunes & App Stores."
If it is turned on, you will not be able to delete songs from an iPhone.
Turn off iTunes Match
Open the Music app. Press botton on Home screen
Delete a song Tap the Songs button at the bottom of the screen. This will give you a list of all songs loaded onto your iPhone. Locate a song you want to remove, then swipe sideways on the track name. A red Delete button will appear. When you click that, the song will be removed.

I think there's a way in itunes (on your computer) by clicking your device on the left hand side of the screen then clicking "music" midscreen. Then make sure "selected playlists, artists, albums and genres" is checked, then go through your library and check which songs you want. This should keep the unwanted songs from downloading automatically when you sync