nongamer

Hi everyone, I'm new to this community and to forums and blogs in general. I have a Lenovo X220 Tablet with 2nd gen core i7 and the following open ports that I'm hoping to somehow use to connect this laptop to an eGPU: PCI express card slot, DisplayPort++, USB 2.0. I also just got an nVidia GTX 970 with 3 open DisplayPorts that I will be installing into my desktop and then connecting it to my new Samsung 4K UN55HU6830FXZA via HDMI 2.0. I wish to connect my laptop to the nVidia card while it's in the desktop to have the nVidia card drive 4K graphics to the 4K TV. I don't plan on using the laptop for gaming, just web surfing, general productivity (not video or image editing), and trading and charting. Everywhere I look online, I only see solutions for connecting laptops to adapter kits to drive graphics via an eGPU. However, I do not wish to have a separate eGPU sitting outside of my desktop. I wish to use the desktop-installed nVidia card while it's in the desktop. I do not plan on simultaneously outputting graphics from the desktop and the laptop to the 4K TV, just switching between the two depending on my productivity needs. However, if there's a way to do picture in picture where both the laptop and desktop can show, I'd like to learn how, but this is not a priority or necessity. My priority is to drive laptop video output to the 4K TV via the nVidia card because my HD3000 internal graphics chip on the X220 laptop is not capable of 4K resolution, even for web surfing, to my understanding. Can someone please guide me on how to do this?