Sure, you can go to row echelon form, and then do back substitution. I would, incidentally, leave out the last column there, as you already know that e = 0. You can save yourself some computations. If the system is consistent (and it better be, because having a polynomial of degree 4 that goes through those four points is definitely possible - just think about Lagrange interpolating polynomials to see that), then I would say you should end up with a 1-parameter family of solutions. What do you get?