Which one? There is A LOT of different CPU options.
Anyway.
IMPORTANT :
1. Any of the CPUs in that system will bottleneck a 280X HARD, this will cause the graphics card to NOT run at near its full power.
2. You would need to upgrade the power supply too as the PSU with that system is NOT anywhere near good enough.
3. I am reasonably sure a card the size of the 280x will not fit in that HP case.
Sorry for the bad news, but putting an HD7970 in that system is just not a good idea.
Now depending on what CPU you actually have in there and the ???resolution??? your monitor is, you can still get a better card.