I reinstalled Linux Mint version 19 this time, and was able to get Elixir 1.9 working. I tried apt install elixir, but still I the latest version it could find was 1.3.3. I removed it, and removed erlang-base.
What eventually worked was to install erlang by apt install erlang-base and then to download the precompiled elixir 1.9 from the elixir-lang website. (I also tried to compile it myself, but this did not work - there was an error finding something from erlang). I was able to add it my PATH and everything is working smoothly now.
The instructions to install the erlang-solutions .deb file did not work for me - I still only got version 1.3.3 of elixir.
