Help with Solving a System of Equations

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Discussion Overview

The discussion revolves around solving a system of equations involving three variables (x, y, z). Participants explore various methods for solving the equations, including algebraic manipulation and computational tools.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • The original poster describes their struggle with solving the system of equations and mentions various unsuccessful attempts, including combining terms and eliminating variables.
  • Some participants suggest using specific computational tools and methods, such as matrix operations in different programming languages (e.g., Matlab, Mathematica).
  • One participant questions the original poster's approach of multiplying an equation by 1, suggesting that it may have led to confusion and proposing that they should instead add equations after multiplying by appropriate constants.
  • Another participant provides an example of how to combine equations to simplify the problem, emphasizing the importance of careful selection of constants for multiplication.
  • A link to an external resource on Gaussian elimination is shared for further explanation of the method.

Areas of Agreement / Disagreement

The discussion includes multiple viewpoints on how to approach the problem, with no clear consensus on the best method. Participants offer differing opinions on the effectiveness of various strategies without resolving the original poster's confusion.

Contextual Notes

Participants express uncertainty about the original poster's methods and terminology, particularly regarding the multiplication of equations. There are unresolved aspects related to the specific steps taken by the original poster and the effectiveness of the suggested methods.

Who May Find This Useful

Individuals seeking assistance with solving systems of equations, particularly in a homework context, as well as those interested in different mathematical techniques and computational approaches.

CanaBra
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I have been trying to solve this problem for a whole week without success, I need help.

Solve the following for x,y and z:

2x+5y-z = 18
7x-y+4z = 22
6x+2y-3z = 0.1x + 0.2y + 0.3z

I have already combined all the terms of eq.#3 and equal it to zero, but it didn't work.
I also, multiplyed eq.#3 by 1 and tried to have a comon x for the other two equations to eliminate x and it didn't work, I've tried many other tatics but it doesn't work.

please help
Thank you
 
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Pari:
Code:
matsolve([2,5,-1;7,-1,4;6-.1,2-.2,-3-.3],[18,22,0]~)

TI-BASIC:
Code:
rref([[2,5,-1,18][7,-1,4,22][6-.1,2-.2,-3-.3,0]])

Matlab:
Code:
linsolve([2 5 -1; 7 -1 4; 6-.1 2-.2 -3-.3], [18; 22; 0])

Mathematica:
Code:
LinearSolve[{{2,5,-1}{7,-1,4}{6-.1,2-.2,-3-.3}},{18,22,0}]
 
Maybe you can show some steps or explain in more detail what your problem is? Show us where you're getting stuck or explain what "it didn't work" means.

-Kerry
 
CanaBra said:
I have been trying to solve this problem for a whole week without success, I need help.

Solve the following for x,y and z:

2x+5y-z = 18
7x-y+4z = 22
6x+2y-3z = 0.1x + 0.2y + 0.3z

I have already combined all the terms of eq.#3 and equal it to zero, but it didn't work.
I also, multiplyed eq.#3 by 1 and tried to have a comon x for the other two equations to eliminate x and it didn't work, I've tried many other tatics but it doesn't work.

please help
Thank you
2x+ 5y- z= 18
7x- y+ 4z= 22
5.9x+ 1.8y- 3.3z= 0 ?

Why in the world would you multiply anything by "1"? Do you mean "10"? That would give you 59x+ 18y- 33z= 0. Getting a "common x" for the other two equations (I guess you mean the same coefficient) would give 14x+ 35y- 7z= 119 and 14x- 5y+ 20z= 110. Subtracting the second equation from the first gives 40y- 27z= 9. What do you mean "it doesn't work"?

The equations above are the
 
HallsofIvy said:
Why in the world would you multiply anything by "1"?

Ahhh - I read it the same way HallsOfIvy did the first time - perhaps you multiplied eq. 3 by eq. 1? Maybe this is the problem - you don't want to multiply, you want to add. Really, you should multiply an equation by a carefully selected constant, then add it to another equation. For example, if you multiply eq. 1 by 4, and add it to eq. 2, you get

[tex]8x + 20y - 4z + 7x - y +4z = 72 + 22[/tex]
or
[tex]15x + 19y = 94[/tex]

Does this help get you started?

-Kerry
 
Last edited:
Thank you everyone,
I was confused, but with your help found the solution to this problem
 

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