I need to convert the line $x+y=0$, $x+y+z=a$ into its symmetric form. I've learned four different methods to convert a line from its general to symmetric form, but three of those methods didn't work in this case. The fourth method (find a point on the line and then find the direction ratios of the line using Cramer's rule) did work, but I feel I shouldn't have been doing that much work to get the answer for this particular question. I feel the answer should have been straight forward and obvious, but I just cannot figure out how.
A cursory glance tells me that the solution of the given set of equation is $z=a$, but clearly $z=a$ is a plane and not a line. I can also say $x=-y$, but I can't figure out how I can relate it with the "$z$ part" of the equation of the line.