The locations are listed in Microsoft Docs on Key Storage and Retrieval. For Local system private the locations are:

• The Microsoft legacy CryptoAPI CSPs store private keys in:

  %ALLUSERSPROFILE%\Application Data\Microsoft\Crypto\RSA\S-1-5-18\
  %ALLUSERSPROFILE%\Application Data\Microsoft\Crypto\DSS\S-1-5-18\
  

• CNG stores private keys in:

  %ALLUSERSPROFILE%\Application Data\Microsoft\Crypto\SystemKeys
  

The locations are listed in Microsoft Docs on Key Storage and Retrieval. 

For Local system private the locations are:

• The Microsoft legacy CryptoAPI CSPs store private keys in:

  %ALLUSERSPROFILE%\Application Data\Microsoft\Crypto\RSA\S-1-5-18\
  %ALLUSERSPROFILE%\Application Data\Microsoft\Crypto\DSS\S-1-5-18\
  

• CNG stores private keys in:

  %ALLUSERSPROFILE%\Application Data\Microsoft\Crypto\SystemKeys
  

In practice they are by default under C:\ProgramData\Microsoft\Crypto\ on Windows 10.