Can I use 16 GB RAM with my MacBook Pro 7,1?
Your Mac needs to meet specific criteria for this to work. In the case of the 2010 Macs, here’s what you must have:

a Mac mini (Mid-2010), a MacBook (Mid-2010) or a 13” MacBook Pro (Mid-2010)
Mac OS X 10.7.5 or later
the latest EFI firmware update for your system
the proper specification memory modules


See Certain 2010 MacBook, MacBook Pro, and Mac mini models join the ’16GB’ MaxRAM club for details.
You will need (2x8GB) 16GB DDR3-1066MHz SODIMM. Anything faster like a DDR3-1333MHz or DDR3-1600MHHz SODIMM will fail to boot the machine.