A system call would not be useful most of the time if it did not return some kind of a value: The file descriptor of an open file, the number of bytes read to a buffer, the system time, etc.
Additionally, the system needs to inform us if an error occurs: A file does not exist, system resources are exhausted, we passed an invalid parameter, etc.
The traditional place to look for information about various system calls under UNIX® systems are the manual pages. FreeBSD describes its system calls in section 2, sometimes in section 3.
For example, open(2) says:
If successful,
open()returns a non-negative integer, termed a file descriptor. It returns-1on failure, and setserrnoto indicate the error.
The assembly language programmer new to UNIX® and FreeBSD
      will immediately ask the puzzling question: Where is
      errno and how do I get to it?
The information presented in the manual pages applies to C programs. The assembly language programmer needs additional information.
Unfortunately, it depends... For most system calls it is in
      EAX, but not for all.  A good
      rule of thumb, when working with a system call for the first
      time, is to look for the return value in EAX.  If it is not there, you need
      further research.
I am aware of one system call that returns the value in
	EDX: SYS_fork.  All others I have
	worked with use EAX.  But I
	have not worked with them all yet.
If you cannot find the answer here or anywhere else, study libc source code and see how it interfaces with the kernel.
Actually, nowhere...
errno is part of the C language, not the
      UNIX® kernel.  When accessing kernel services directly, the
      error code is returned in EAX, the same register the proper
      return value generally ends up in.
This makes perfect sense. If there is no error, there is no error code. If there is an error, there is no return value. One register can contain either.
When using the standard FreeBSD calling convention, the
      carry flag is cleared upon
      success, set upon failure.
When using the Linux emulation mode, the signed value in
      EAX is non-negative upon
      success, and contains the return value.  In case of an error,
      the value is negative, i.e., -errno.
All FreeBSD documents are available for download at https://download.freebsd.org/ftp/doc/
Questions that are not answered by the
    documentation may be
    sent to <freebsd-questions@FreeBSD.org>.
    Send questions about this document to <freebsd-doc@FreeBSD.org>.