You walked it through a lot further than I generally will (and noticed something interesting as a result).The situation is even kinkier than what WBahn suggests. You did indeed make an error in your initial equations, and propagated that error to the last equations shown:
Actually, I didn't. I haven't worked it through to a solution. Just stated the process that I almost always use (and have gotten bit on numerous occasions when I didn't). I never assume that the answer I get is correct -- I know the kinds of mistakes I have made and have seen others make to justify that level of hubris. So I always ask if the answer makes sense (and, of course, I've already confirmed that the units work out since I religiously track my units throughout my work). But then I usually plug my solution back into the problem -- or at least a limiting case of the problem -- to validate it. Or I solve the problem via a different means, if that's simpler. Thus if my solution doesn't match someone else's (such as the author or a student or a coworker or a customer) then I have some confidence that mine is correct. But I then check theirs to confirm that. And there have been times when it turned out that the other solution was correct, "too", and then I've spent significant time trying to understand the situation. In the end I've always tracked it down, though I recall one time that took several days to do so -- sometimes I was right and sometimes I wasn't, but I've always learned something valuable in the process.In post #1, your second equation began with j4(I2 + I1); you fixed that in post #4. The solution you get is the same solution I get. It would appear that "correct" answer you have been given is not correct after all. Perhaps somebody else will chime in here and verify.
Edit: WBahn beat me to it by 3 minutes.
by Kate Smith
by Luke James