Delete please Please delete. (Edited on Friday 13th 2:53 p.m.) 1. The problem statement, all variables and given/known data ANYTHING that looks similar to solving these by addition/elimination: Equation One: 3x - y + 2z = 1 Equation Two: 2x +3y +3z = 4 Equation Three: x + y - 4z = -9 The book's answers: (-1, 0, 2) The attempt at a solution Okay here is what I did in order to observe: Re-do the problem 3 times in 3 different ways. Method 1: Eliminate X first -- in which I got the correct answers. Method 2: Eliminate Y first -- in which I got the correct answers. Method 3: Booboo. I got a fraction when the first Y was solved for. I got y = 42/116 or 21/58 Comments: So why does it get messed up when I decide to eliminate Z first? How do I know which variable I should eliminate first in order to get the correct answer? Step 1. Add equation 1 to equation 2: 1a.--> 3(3x - y + 2z) = 3(1) 1b.--> 9x -3y + 6z = 3 2a.--> -2(2x +3y +3z) = -2(4) 2b.--> -4x -6y -6z = -8 Add equation 1b and 2b to get equation 4: 5x -9y = -8 (Edit at 3:52 p.m. Okay... hmm I just picked this error up... Step 2: Add equation 1 to equation 3: 1a.--> -4(3x -y +2z) = -4(1) 1c.--> -12x +4y -8z = -4 3a.--> -2(x +y -4z) = -2(-9) 3c.--> -2x -2y +8z = 18 Add equation 1c and 2c to get equation 5: -14x +2y = 14 Step 3: Treat equations 4 and 5 as if it were a system of two systems of linear equations. Add equation 4 to 5: 4a.--> -14(5x -9y) = -14 (-8) 4b.--> -70x +126y = 112 5a.--> -5(-14x +2y) = -5(14) 5b.--> 70x -10y = -70 Add equation 4b to 5b to get the Y variable: Y=42/116 or 21/58 COMMENTS: Does it matter which variable you choose to solve for? What concepts could I be missing? I've re-read the instructions several times -- I've spent 3 days already trying to re-try with no luck. I am sure, unless my eyes are playing tricks on me, is that it is stated it should not matter which variable you eliminate first as you will always get the same answer.