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(Edited on Friday 13th 2:53 p.m.) I just want to know, if there are anyone out there who knows why I keep getting fractions after adding 2 equations to solve for one of the variables. For example, Z or Y or X would equal 23/20 and the book's answer would be a whole number.

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.

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# I keep getting fractions trying to solve Systems of Linear Equations with 3 variables

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