Find three vectors p, v, w in R^4, such that the solutions to the system

w+3x+3y+2z=1

2w+6x+9y+5z=5

-w-3x+3y=5

have the form p + \lambda v + \mu w, with \lambda, \mu in R.

I assumed one would get rid of the z, and be left with two equations to solve three unknowns, so would write everything in terms of one vector, but simplifying the first two equations gives the third

So now I'm completely bewildered...