G SKill FAQs:
Q:
I want to install more memory, in addition to my existing memory kit. What are my options?
A:
We do not recommend mixing memory kits, regardless of brand or model.
By mixing memory kits together, there may be compatibility issues such as unable to boot or unable to operate at rated specifications.
Each of our memory kit are thoroughly tested to ensure compatibility within each memory kit. And because we have not tested our memory kit with your existing memory kit, we cannot guarantee compatibility when multiple kits are used.
http://www.gskill.com/en/faq/DRAM_Memory
Corsair FAQs:
Which Corsair Memory modules will work with my existing modules?
We strongly recommend matching the module part number as closely as possible in order to ensure the greatest chance of compatibility. Even if you match part numbers properly, we can't make guarantees as to their performance as the modules weren't tested together. Also be aware that when using two kits of memory together, you may need to reduce the speed of the memory due to motherboard chipset limitations.
From the above two memory FAQs, you can see using two kits are not guaranteed to work. Plus your 2133MHz speed is only for overclocked systems. Your chances for getting two kits to work together is not very good.