The system of equations     −2x+y+z=a      x−2y+z=b      x+y−2z=chas

When we add three equations, we get 0=a+b+c . Thus, the system does not have a solution if  a+b+c≠0 . If a+b+c=0 , the system has infinite number of solutions given by                  x=13(3k−2a−b)                   y=13(3k−a−2b)                  z=k Wherek∈C .