vgremove vgsystem2
vgextend vgsystem /dev/sdb1
I am assuming that /dev/sba1 on the last line actually means /dev/sdb1
Edit 1
You don't need to run partprobe after the reboot. But it wouldn't hurt.
pvscan tells you that you have 2 lvm2 devices (/dev/sda1 and /dev/sdb1). In addition to that sda1 is fully used for volume group vgsystem.
Not surprisingly pvcreate fails because /dev/sda1 is already a physical volume.
Not surprisingly vgcreate fails because vgsystem already exists.
/dev/sda1 looks a bit small. Do you have /dev/sda2 or perhaps unpartitioned space on /dev/sda?
I am not sure what you are trying to achieve
If you want to remove VG vgsystem from /dev/sda1 use pvremove vgsystem
If you want your 2 devices to be treated as a single logical volume you need to expand volume group vgsystem to sdb1 and then create a logical volume:
vgextend vgsystem /dev/sdb1
lvcreate -l 100%VG -n lvsystem vgsystem
then you should be able to make a filesystem on /dev/lvsystem, mount it and use it.
Edit 2
Umm, I haven't forsaken you. Please re-read what I wrote between Edit 1 and Edit 2. Did you try running any of the commands? What was the output? What is your answer for "Do you have /dev/sda2 or perhaps unpartitioned space on /dev/sda?"?
It would be nice to know what exactly are you trying to achieve. This will help me help you.