how to restore Mac system

First, What to do before you sell, give away, or trade in your Mac. To restore to factory state, you need to know what vintage your iMac is from. If it is pre-Late-2011, then you must use the Software Restore DVDs that came with the computer. If the iMac is from Late-2011 or later, then do the following:

Internet/Network Recovery of El Capitan or Later on a Clean Disk

     If possible, back up your files before proceeding.

1. Restart the computer. Immediately, at or before the chime, hold down the (Command-Option-Shift-R) keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the target drive (out-dented entry w/type and size) from the side list.
5. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to APFS (SSDs, only if installing Mojave or Catalina ) or Mac OS Extended, (Journaled.)
8. Provide a volume name, usually "Macintosh HD."
9. Click on the Apply button, then click on the Done button when it activates.
10. Quit Disk Utility and return to the Utility Menu.
11. Select Install OS X and click on the Continue button.

This should install the version of OS X that was pre-installed at the factory. After the installation has completed it will automatically boot into the Setup Assistant. If you are giving, selling, or trading the computer, then at this point you should simply shut down the computer - do not continue with the setup.

• Reboot holding down Command-R
• From Utilities menu, chose Disk Utility and then to erase the internal volume (eg 'Macintosh HD')
• Once erased, quit out of Disk Utility and select to install macOS
• Done

You will, of course, lose all your personally but the Mac will be restored to factory settings.