- #1

Raizy

- 107

- 0

**Delete please**

Please delete.

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.

(Edited on Friday 13th 2:53 p.m.)

## Homework Statement

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 21/58COMMENTS:

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.

Last edited: