1. The problem statement, all variables and given/known data given the planes with equations: x + y + 7z = -7 2x + 3y + 17z = -16 x + 2y + (a^2 + 1) z = 3a find values for the constant a for which: -there are no solutions -the planes meet in a line. in this case find the parametric equation of the line -meet at a point. then find the parametric equation of the point. 2. Relevant equations gaussian elimination? I dont think there are any. =S 3. The attempt at a solution I put the planes into an augmented matrix, and then into echelon form, and got (I think its correct) the general solution, which is attached. From the I can read off the equation of the line, right? The parts I'm really stuck on are parts one and three. I realise that for the planes to meet in a point, there has to be 3 pivots but beyond that I'm a bit stumped. Well actually, I have a bit of a clue for part one, that a =/= 3 because then 0z = 18 which is inconsistent. is that right? But for part 3, I'm not sure how to do it, really.