In case Trefor Jones reads this: I replied to your email, Trefor, but it came back as undeliverable. Here's what I said. Well, Trefor, I've played around with two of Excel's functions and have to ask: are you sure you've given me the right coefficients? I did what you did and derived a fifth equation: simple and satisfies the MINVERSE and MMULT requirements. I get answers: a = 16 b = 4 c = 0 d = 16 e = 16 But these values do not satisfy the equations: instead of the RHS values you gave for equations 1 - 4, these answers give me 16 20 16 -4 I then tried the SOLVER routine and ended up with similar values: a = 15.90 b = 3.79 c = 0.16 d = 16 e = 16.15 16.16 21.2 16.4 -3.76 I'll happily work on this a bit more, Trefor: just confirm your data and we'll see if we can make any more progress. Best wishes DW