pigz -dc backup2_week1_system.tar.gz | tar vxf - FILE
where FILE is the file to extract. For example
pigz -dc backup2_week1_system.tar.gz | tar vxf - bob
Will extract the bob directory (e.g. /home/bob) from backup2_week1_system.tar.gz. Note that you don't need the z flag because pigz will already decompress the gzip'd portion.