Is it possible to hide/encode/encrypt the php file/source code, and let others have the system installed and run on their machine?
Yes, you can definitely hide/encode/encrypt the php source code and 'others' can install it on their machine. You could use the below tools to achieve the same.
But these 'others' can also decode/decrypt the source code using other tools and services found online. So you cannot 100% protect your code, what you can do is, make it tougher for someone to reverse engineer your code.
Most of these tools above support Encoding and Obfuscating.
You can choose to use both (Encoding and Obfuscating) or either one, depending on your needs.