Here's the question.
Solve the simultaneous equations $$ab + c + d = 3$$ $$bc + d + a = 5$$ $$cd + a + b = 2$$ $$da + b + c = 6$$ where $a, b, c, d$ are real numbers.
Obviously there's a lot of ways to look at this, but I always find myselfat a dead end; either ending up with what I started with or getting a complicated mess. Is there a systematic way to approach this or is there just a niche technique required to answer this specific question? Also, is there a way of knowing before whether going through a method is going to provide new information of if I'm going to end up with something like $a=a$?
