The 1050 Ti will be a good match for 7700K so you shouldn't have any problems there. I assume that the R7 is the integrated graphics so need to know what mobo you have so we can figure out what expansion slots are on the mobo. Specifically, do you have a PCI-e x16 slot and what revision is it. Also need to know what kind of Power Supply Unit (PSU) you have so we can figure out how much power is available.
To determine slot availability you can
■ Run this program and tell us what motherboard model it is. The manufacturer and model is found on the mainboard tab. The program is free and safe.
http://www.cpuid.com/softwares/cpu-z.html■ Look at the mobo and see if there is PCI-e x16 slot. Here is a pic showing what it would look like, pay attention to the gap widths in the slot and if there is a locking mechanism at one end.
http://www.playtool.com/pages/vidslots/mballslots.jpg■ Look up the information in either the computer or motherboard manual
For the PSU you can open up the case and look for a label on the PSU. It will state the wattage on the label and the amps for the 12V rail. Or you can take a picture of the label and post a link and I can figure it out.
I don't see the 1050 Ti being an issue, it is only a 75W GPU but unfortunately many pre-builts come with low quality, low power PSU's so it has to be checked out.