Help with Solving a System of Equations

[CanaBra]

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

 

[CRGreathouse]

Pari:

matsolve([2,5,-1;7,-1,4;6-.1,2-.2,-3-.3],[18,22,0]~)

TI-BASIC:

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

Matlab:

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

Mathematica:

LinearSolve[{{2,5,-1}{7,-1,4}{6-.1,2-.2,-3-.3}},{18,22,0}]

 

[KLoux]

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

 

[HallsofIvy]

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

 

[KLoux]

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

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

Does this help get you started?

-Kerry

 

[hotvette]

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

See link for explanation of Gauss elimination:

http://en.wikipedia.org/wiki/Gaussian_elimination

 

[CanaBra]

Thank you everyone,
I was confused, but with your help found the solution to this problem