Generating random points from intersection of multiple spaces in _R_8

I am trying to write a Python code to sample 50 random points from the intersection of five subspaces in R⁸. The spaces are three hypercylinders (x₁²+x₂²=4; x₃²+x₄²=4; x₅²+x₆²=4) and two linear spaces (x₁+x₃+x₅+x₇=4; x₂+x₄+x₆+x₈=0).

For all I know is that the intersection can be an infinite set and finding roots of functions as mentioned in Python: Intersection of Spheres may not be feasible.

Also, I tried implementing from Sample random points over intersection if surfaces but couldn't get much.

I have recently started to use Python and request you to pardon me for my rookie mistakes.