Actually the answer can be generated by a single PowerShell statement :-)
$(ls MySystemName*.* | measure -s -pr Length).Sum / 1gb
The answer is the number of gigabytes given by a Double number.
A more readable version of the statement without aliases is
$(Get-ChildItem MySystemName*.* | Measure-Object -Sum -Property Length).Sum / 1GB
The statement is invoked with the location in the backup folder.
If a sum of sizes from more than one location the amounts can be taken from UNC paths and addeded up
($(ls '\\SERVER01.sqladmin.lan\Y$\SQL Server Backup\SystemOne*.bak' | measure -s -pr Length).Sum + $(ls '\\SERVER02.sqladmin.lan\Y$\SQL Server Backup\SystemOne*.bak'| measure -s -pr Length).Sum) / 1gb
In this example the default shares are used in the UNC path.