Develop a Ruby on Rails application that serves as a task management system. Users should be able to create, edit, delete, and mark tasks as completed. Integrate the app with an SQLite database for storing task data.

To create a Ruby on Rails application that serves as a task management system, follow these steps:

1. Install Ruby and Rails: Make sure you have Ruby and Rails installed on your machine. You can check if they are installed by running `ruby -v` and `rails -v` in the terminal. If not, install them from https://www.ruby-lang.org/en/downloads/ and http://installrails.com/.

2. Create a new Rails app: Run the following command to create a new Rails app with SQLite as the default database:
```
rails new task_management_system
```

3. Change into the newly created directory:
```
cd task_management_system
```

4. Generate a scaffold for tasks: Run the following command to generate a scaffold for tasks with title, description, and completed attributes:
```
rails generate scaffold Task title:string description:text completed:boolean
```

5. Migrate the database: Run the following command to create the tasks table in the SQLite database:
```
rails db:migrate
```

6. Add validations to the Task model: Open the file `app/models/task.rb` and add the following lines inside the `class Task < ApplicationRecord` block:
```ruby
validates :title, presence: true
validates :description, presence: true
```

7. Update the tasks controller: Open the file `app/controllers/tasks_controller.rb` and update the `create` action to redirect to the root path after creating a task:
```ruby
def create
  @task = Task.new(task_params)

  respond_to do |format|
    if @task.save
      format.html { redirect_to root_path, notice: 'Task was successfully created.' }
      format.json { render :show, status: :created, location: @task }
    else
      format.html { render :new }
      format.json { render json: @task.errors, status: :unprocessable_entity }
    end
  end
end
```

8. Update the routes file: Open the file `config/routes.rb` and update it to set the root path to the tasks index:
```ruby
Rails.application.routes.draw do
  resources :tasks
  root 'tasks#index'
end
```

9. Start the Rails server: Run the following command to start the Rails server:
```
rails server
```

10. Access the app in your browser: Open your browser and navigate to http://localhost:3000/ to access the task management system.

Now you have a basic Ruby on Rails application that serves as a task management system with SQLite database integration. Users can create, edit, delete, and mark tasks as completed.