Linear Algebra

Notice equation 2 has left side exactly $2 \times$ (equation 1): $4x - 2y + 6z = 2(2x - y + 3z) = 2(1) = 2$. For inconsistency, $c \neq 2$. If $c = 0$, the system has no solution. (Testing $c = 0$ yields contradiction $2=0$).