Maybe the elixir:1.9.1-slim image doesn’t have the build tools installed?

docker run --rm -it elixir:1.9.1-slim /bin/bash

Unable to find image 'elixir:1.9.1-slim' locally
1.9.1-slim: Pulling from library/elixir
092586df9206: Already exists
1ea657b85b1b: Pull complete
88e54a5e27b9: Pull complete
Digest: sha256:2db029a79b6cc18dc598d37257fabe2cc6219d105acf6f4a68ec9cfc8120d102
Status: Downloaded newer image for elixir:1.9.1-slim

root@b851f47dd24d:/# make
bash: make: command not found
root@b851f47dd24d:/# 

elixir:1.9.1 has it though:

docker run --rm -it elixir:1.9.1 /bin/bash
root@1193ae2771b8:/# make
make: *** No targets specified and no makefile found.  Stop.
root@1193ae2771b8:/#

So maybe you could try something like

name: Elixir CI

on: push

jobs:
  build:

    runs-on: ubuntu-latest

    container:
-     image: elixir:1.9.1-slim
+     image: elixir:1.9.1

    steps:
    - uses: actions/checkout@v1
    - name: Install Dependencies
      run: |
        mix local.rebar --force
        mix local.hex --force
        mix deps.get
    - name: Run Tests
      run: mix test