Jibberish-example.txt S2013 This example solves x + y + z = 1, y + 3z = 4, z = 5. Back-Substitution by the jibberish method ========================================= x + y + z = 1, y + 3z = 4, z = 5. y=4-3(5)=-11 x=1-5-(-11)=7 What's wrong with it? (1) No answer; (2) No readable details. And if there was a mistake, who could find it? Back-Substitution by frame sequences ==================================== x + y + z = 1, y + 3z = 4, z = 5. x + y + z = 1, y = -11, combo(3,2,-3) z = 5. x + y = -4, combo(3,1,-1) y = -11, z = 5. x = 7, combo(2,1,-1) y = -11, z = 5. The answer is x=7, y=-11, z=5, steps documented above. Arguments for and against ========================= 1. Jibberish is faster. 2. Jibberish can silently get the wrong answer. 3. Jibberish fails miserably when there are free variables. It is problematic to check a free variable answer. 4. Frame sequences take too long to write. 5. Frame sequences get the right answer even if there are free variables.