Error: ANS1705E System Writer(s) 'system writer' do(es) not exist.

If System Writers is not showing in "vssadmin list writers", there is some issue with permission on "%windir%\winsxs\temp\PendingRenames".
To allow appropriate permission, use below mentioned commands.

-Open cmd
-Go to %windir%\winsxs
-Type the following commands to allow permission:

Takeown /f %windir%\winsxs\temp\PendingRenames /a
icacls %windir%\winsxs\temp\PendingRenames /grant "NT AUTHORITY\SYSTEM:(RX)"
icacls %windir%\winsxs\temp\PendingRenames /grant "NT Service\trustedinstaller:(F)"
icacls %windir%\winsxs\temp\PendingRenames /grant BUILTIN\Users:(RX)
Takeown /f %windir%\winsxs\filemaps\* /a
icacls %windir%\winsxs\filemaps\*.* /grant "NT AUTHORITY\SYSTEM:(RX)"
icacls %windir%\winsxs\filemaps\*.* /grant "NT Service\trustedinstaller:(F)"
icacls %windir%\winsxs\filemaps\*.* /grant BUILTIN\Users:(RX)
net stop cryptsvc
net start cryptsvc

Now again run "vssadmin list writers" in command prompt, "system writers" should be visible there.