While I coded up my solution to Project Euler 102 using the article I read on Wolfram Alpha, I was trying to derive the steps they took to solve for a, b in the article – and I found it much more intuitive to just get to a, b by simply inverting the 2 x 2 matrix, and multiplying that matrix inverse by a vector.
I was noodling around with the math to see how it works, and here are the notes….