The obvious question is: What motherboard do you have? Considering that you did not post that, I would guess that your system is not homebuilt. To get the answer you asked for, please provide at least the make and model of computer. You can download CPU-Z and show us the motherboard details. Oh - your title says Gateway RS780. You should have an x16 slot at I can't tell which PCIe level.
However, it may not matter much to your answer. A PCIe 3.0 x16 card will run in a PCIe 2.0 x8 slot. So unless your motherboard has an unusually poor graphics support (like some business-oriented machines), you should be able to use most modern cards.