rEMOVE OPERATING SYSTEM ON DUAL BOOT

I am giving my old system to my daughter but it is set up to dual boot between Vista and 7.

How do I delete Vista and leave the system with just windows 7 installed?

I personally would before giving my old system to my daughter, a nice clean install.
To clean install:
1) Clean the HD Drive, using Step one in this tutorial:
SSD / HDD : Optimize for Windows Reinstallation
than
2a) clean install with the OEM manufacturer's Recovery Disk.
2b) Clean Install Windows 7

2c) UEFI (Unified Extensible Firmware Interface) - Install Windows 7 with

If you have a Win7 install that you like that's fast and never hangs, we can help you remove Vista and merge its disk space with Win7. Post back a screenshot of Disk Management - Post a Screen Capture Image.

However if this is preinstalled Win7 that came with the PC and was never given a Clean Reinstall - Factory OEM Windows 7 to lose the bloatware and duplicate utilties which interfere with better versions built into Win7, I would use this opportunity with our help to wipe the HD and do a perfect install.

If it's somewhere in between where it needs to have some kinks ironed out or you'd prefer just to Clean Up Factory Bloatware then we can help you with that too. Just read the blue links and decide which you prefer.

Power down to unplug the Vista HD, swap its cable to Win7 HD so it becomes Disk0.

Then from the booted Win7 disk or System Repair Disk run Startup Repair - Run up to 3 Separate Times until Win7 boots and holds the System flag.

You can then plug back in the other HD, mark it Inactive to delete it in Disk Mgmt, repartition as desired.

I dont' know what the F Programs partition but if it is your installed Win7 programs this is not recommended and is besides sitting in the preferred lower HD address where WIn7 can benefit from faster read and write speeds. So I would reinstall any programs wrongly installed outside of C, delete F and resize C into the space using Partition Wizard CD to Resize Partition - Video Help.