# System of equations 4 variable

1. Mar 10, 2009

### synergix

1. The problem statement, all variables and given/known data
Solve
2w + 2x - 5y + z = -16 (1)
-w + x + 6y - z = 15 (2)
2w - x + y + 6z = 3 (3)
w + x + 2y - z = 7 (4)

3. The attempt at a solution

(2) + (4) = 2x + 8y - 2z = 22 (5)

2(2) + (3)= x + 13y + 4z = 33(6)

2(2) + (1)= 4x + 7y - z = 14 (7)
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-2(6) + (5)= -18y - 10z = -44 (8)

-4(6) + (7)= -45y - 17z = -118(9)

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-17(8) + 10 (9)= y = 432/90 (10)

then start substituting. is this the best way to do it I found it very tedious and my answers didnt check I obviously made a mistake somewhere but I cant say I know what I did wrong (w,x,y,z) (62/85,207/85,24/5,98/17)

2. Mar 10, 2009

### synergix

I found my mistake y=3

3. Mar 10, 2009

### buffordboy23

The best way to solve the problem depends on your mathematical background. It seems evident that you don't have any experience with matrices, or else you would have used likely used Gaussian elimination (which is usually quicker, especially with a computer).

The work for you to learn this tool (Gaussian elimination) in solving systems of linear equations should be relatively easy for you to obtain with your current background. If your interested, see the link with example: http://en.wikipedia.org/wiki/Gaussian_elimination#Example

4. Mar 10, 2009

### arildno

(5), (6) ,(7), (8), (9) are right.

In (10), however, the y-coefficient, (-17)*(-18)-45*10=-144, rather than -90. (RHS equals -432.

Thus, the y-value out to be 432/144=3

Thus, z=-1, and you can calculate x and w yourself.

5. Mar 10, 2009

### synergix

actually in my math course matrices are not covered for whatever reason. we stop right before the chapter on matrices. and completely skip it. I will have to ask my instructor why.

6. Mar 10, 2009

### synergix

yes somehow I got 90 from that subtraction not sure how but I figured it out now thx.