[Aaron.Graeve]

I just finished up the solutions problems in the original post, using three pages of paper in the process. Ether, your solutions check out fine to me (albeit I have very well could have missed something). I also see what you mean by the solution being messy. I think the derivation was messier. To anyone wondering, I solved it each time with a set of matrices and Cramer's Rule. Cramer's rule is both really cool and useful. I advise you all to go check it out. I may try my hand at proving the others tomorrow. Ether, as I stated previously, this is a very good challenge. Thank you.