You have a PCI-e 16x slot so you can fit most GPUs, but you have a weak CPU and a small power supply that may use non-standard connectors(Thanks HP....)
I assume you are planning to game since you are looking at an R9 280? If thats the case then you are going to want to get a better power supply for the system so you can support a real GPU, and likely port it over to a different case, HP cases are small and cramped, they are fine for the original equipment but if you put a real GPU in there its not going to be able to get rid of the heat well.
You also don't have a very strong CPU so there are many games where you would not be able to make full use of something as strong as an R9 280.
Info on the system for those who come later
http://h20565.www2.hp.com/portal/site/hpsc/template.PAGE/public/kb/docDisplay?javax.portlet.begCacheTok=com.vignette.cachetoken&javax.portlet.endCacheTok=com.vignette.cachetoken&javax.portlet.prp_ba847bafb2a2d782fcbb0710b053ce01=wsrp-navigationalState%3DdocId%3Demr_na-c03544617-2%7CdocLocale%3D%7CcalledBy%3D&javax.portlet.tpst=ba847bafb2a2d782fcbb0710b053ce01&sp4ts.oid=5279181&ac.admitted=1411313830466.876444892.492883150