Install Erlang Dependencies

Note: This assumes you are using GTK, if not, choose a different version of the libwx or you'll end up installing all of GTK. If you aren't using a window manager, you don't need WX at all, but you'll miss out on some cool built in GUIs.

sudo apt-get install build-essential libncurses5-dev libssl-dev libwxgtk3.0-dev

Download and compile Erlang

wget http://erlang.org/download/otp_src_20.0.tar.gz
tar -xf otp_src_20.0.tar.gz
cd otp_src_20.0/
export ERL_TOP=`pwd`
./configure
make

Install Erlang

I went ahead and let it install Erlang to the system paths

sudo make install
cd ..

Download and compile Elixir

wget https://github.com/elixir-lang/elixir/archive/v1.5.1.tar.gz
tar -xf v1.5.1.tar.gz
cd elixir-1.5.1/
export LANG="en_US.UTF-8" # Elixir complains if you don't use UTF-8
make

Install Elixir

I let this install to the system paths as well

sudo make install

Test it

At this point you should be good to go, try running a shell with

iex