Help with Solving a System of Equations

In summary, the conversation was about a person who had been trying to solve a math problem for a week without success and needed help. The problem involved solving for x, y, and z in a system of three equations. The person had already tried combining and multiplying equations, but it didn't work. They were then given suggestions on how to approach the problem, including using Gaussian elimination. In the end, with the help of others, the person was able to solve the problem.
  • #1
CanaBra
14
0
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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  • #2
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}]
 
  • #3
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
 
  • #4
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
 
  • #5
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:
  • #7
Thank you everyone,
I was confused, but with your help found the solution to this problem
 

FAQ: Help with Solving a System of Equations

What is a system of equations?

A system of equations is a set of two or more equations with multiple variables that are related to each other. The solution to a system of equations is the values of the variables that make all of the equations true simultaneously.

How do you solve a system of equations?

There are various methods for solving a system of equations, including substitution, elimination, and graphing. The method used will depend on the specific equations and variables involved.

What is the purpose of solving a system of equations?

The purpose of solving a system of equations is to find the values of the variables that satisfy all of the given equations. This can be useful in solving real-world problems, such as finding the intersection point of two lines or determining the optimal solution to a system of linear equations.

Can a system of equations have more than one solution?

Yes, a system of equations can have one, infinite, or no solutions. This depends on the nature of the equations and how they relate to each other. For example, two parallel lines will have no solution, while two overlapping lines will have infinite solutions.

How do you know if a system of equations has no solution?

A system of equations has no solution if the equations are contradictory, meaning they cannot both be true at the same time. This can be determined by graphing the equations and seeing if they intersect at any point, or by solving the equations and reaching a contradiction, such as 1 = 2.

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