# Gaussian elimination

1. Feb 16, 2016

### Physicaa

1. The problem statement, all variables and given/known data
I started with the following equations :

3w+2x+3y+z=76
w+2x+2y+z=59
w/2+x+y+z/4=21

2. Relevant equations

Gaussian elimination
3. The attempt at a solution
So I got the following after applying Gauss' method :

3w+2x+3y+z=76

-4x-3y-2z=-101

3/2z=51
which gives z=34

Then I get y=11-(4/3)x

w=3+2/3x

Does it make any sense ? I compared it with wolfram and it seems like the only good thing that I got was the z=34...

2. Feb 16, 2016

### vela

Staff Emeritus
You need to show your work. If all you do is post the wrong answer you got at the end, the best we can say is that you messed up somewhere.

3. Feb 16, 2016

### Physicaa

4. Feb 16, 2016

### Samy_A

Why do you think your solution is wrong?
Dit you try to substitute what you found for w,y,z in the three equations to check if they add up?

5. Feb 16, 2016

### Physicaa

I think it's wrong because wolfram gives me something different.

Here : http://www.wolframalpha.com/widgets/view.jsp?id=ae438682ce61743f90d4693c497621b7

Try this and see. The only good thing that I get is 34.

6. Feb 16, 2016

### Samy_A

That link doesn't show any equation or solution.
Forget Wolfram for a moment, just try your solution: check if it fits the three equations.

EDIT: I copy pasted the equations in the link you gave and got this result:

Is this wat Wolfram told you? If so, how does this compare to your solution?

7. Feb 16, 2016

### Physicaa

Ok so Im going to compute the following equations z=34, y=11-4/3x w=3+2/3x, x=33/4-3/4y

8. Feb 16, 2016

### Samy_A

Now you are turning in circles: y in terms of x, x in terms of y: that doesn't make much sense.

$w=3+\frac{2}{3}x$
$y=11-\frac{4}{3}x$
$z=34$
Plug these values in the equations and see if it all adds up or not.

9. Feb 16, 2016

### Physicaa

I was finally able to make the equations be true by pluggin these equations :

z=34, y=t, x=(33-3t)/4 , w=(17-t)/2

It seems to work with these.

10. Feb 16, 2016

### Samy_A

Your first solution was correct (you should have checked). This one is correct (although I don't see why you need t and don't just use y). The one from Wolfram is also correct.
You can express w and y in terms of x, as you did in the first post. Or x and w in terms of y, as you do here. Wolfram gave x and y in terms of w.

11. Feb 16, 2016

### Ray Vickson

Since you have 3 equations in 4 unknowns, you can express solutions in many ways. You can solve for (x,y,z) in terms of w (to get x = -9/2+3/2*w, y = 17-2*w, z = 34), or you can solve for (x,z,w) in terms of y or for (y,z,w) in terms of x. (However, if you try to solve for (x,y,w) in terms of z you will find that something goes wrong, so you cannot do it!)