Question

When solving for a system of equations, if you get an answer of 6=0, what does this solution mean regarding the solution to the system ?

Answer 1

It means that graph is inconsistent. Most likely it is a no solution

Answer 2

it means the system is inconsistent, which is another way to way, there's no solution, namely, both graphs do not intersect ever, and therefore there's no common point with such x,y pair for both.