How to use Tesla k20c + Quadro 400 hardware configuration (Tesla for CUDA, Quadro for monitor)

I have Ubuntu 16.04 installed on my computer. Hardware includes two Nvidia’s GPU: Quadro 400 and a Tesla K20c.
I would like to use the Tesla card for computations with CUDA and Quadro 400 just for the monitor.
The problem is that I need to install an Nvidia driver of version higher than 367 for the Tesla in order to use CudaTollKit 8.0, while my Quadro card does not work with this driver. The latest driver for Quadro 400 is 340, but this driver version is not suitable for cuda-8.0.
I did not find the way to install both drivers in the system and base on the searching in the Internet it seems almost impossible.
How can I use my hardware for the purposes described above? I would appreciate any suggestions.

You can’t install 2 drivers and you cannot use both of these cards together. Replace the Quadro 400 with a newer card.