At k= -2 your system has the form

  x +  y +  z = 0
-2x +  y - 2z = -6
      2y      = -4.


Last equation gives y = -2  and, after substituting this value of y into two other equations, gives you the system 

  x +  z =  2
-2x - 2z = -4 


It is equivalent to the system

  x + z = 2
  x + z = 2,


Which is, actually, ONE equation

  x + z = 2.


Thus the equations in 3D space of the straight line under the question are these two equations

   y = -2,
   x + z = 2.


It is the answer in rectangular form.


In vector form the parametric equation for this straight line is 

   V(t) = (t,-2,2-t),  where t is the parameter  (= any real number).