The System partition, which you can see is marked as Active, holds the boot files. You will not be able to boot if it is deleted.
You can rebuild your boot system to ignore that partition and put the boot files in the Windows 7 partition. To do that, you will have to show the Windows 7 partition as active and then do a startup repair 3 times. The first run might just reboot, but the second run you should bypass the reboot option and go to the Start Repair option.
It can be dangerous when you attempt to move the leading edge of a partition, so if you do that, be careful and have backups, hopefully an image you could restore in case of problems.