1. The problem statement, all variables and given/known data The assignment is to find all values of k (in R) for which the system has 0 solutions, 1 solution and infinite solutions. If there are infinite solutions, find the amount of free variables. The system of linear equations: kx + (k+1)y + z = 0 kx + y + (k+1)z = 0 2kx + y + z = k+1 2. Relevant equations Now k=-1 3. The attempt at a solution So I was correct that this system is undefined when k=0. Then I thought this system had infinite solution when k =/= 0. But here I'm wrong. Apparently if k=-1 then there are infinite solution with one free variable. However, when I plug in -1 then all solutions are -1/2. I don't understand why this is infinite. I did my row operations as practise.