1. The problem statement, all variables and given/known data What conditions do x, y and z need to fulfill for the system of equations to be consistent? 2. Relevant equations 2a + 3b + 5c = x a + 3c = y a - b + c = z 3. The attempt at a solution Not quite sure. The notion of consistency was never discussed in class, nor is it addressed in the linear algebra text. I understand that it simply means having some sort of solution, and that inconsistency means not having any sort of solution - but examples almost always give integers on the right sides of the equations so that you can reduce the rows and see if there's a contradiction (such as 0+0+0=1) or not. Is it just "If a, b and c are zero, then x, y and z must not be other than zero" or something of that nature?