Solving the system of equations

[charlesjoy]

Can you verify my work? I am stuck on the following problem.

Solve the system of equations. IF the system is dependent, express solutions in terms of a parameter z

x - y + 5z = -9
5x + z = -1
x + 4y + z =15

Here is what I have done:

Step #1

5x + z = -1
x - y + 5z = -9
x + 4y + z =15

Step #2

-10x -2y - 2z = 2 add x - y + 5z = -9 comes out to -9x -3y + 3z = -7

Step #3

5x + z = -1
-9X -3y + 3z = -7
x + 4y + z =15

Step #4

5x + z = -1
-9X -3y + 3z = -7
4x + 4y = -14


This is where I am stuck

 

[Deleted member 4993]

Can you verify my work? I am stuck on the following problem.

Solve the system of equations. IF the system is dependent, express solutions in terms of a parameter z

x - y + 5z = -9
5x + z = -1
x + 4y + z =15

Here is what I have done:

Step #1

5x + z = -1
x - y + 5z = -9
x + 4y + z =15

Step #2

-10x -2y - 2z = 2 add x - y + 5z = -9 comes out to -9x -3y + 3z = -7

Step #3

5x + z = -1
-9X -3y + 3z = -7
x + 4y + z =15

Step #4

5x + z = -1
-9X -3y + 3z = -7
4x + 4y = -14


This is where I am stuck

Look at Galactus's answer to your previous problem - follow the steps accordingly.

You are not following proper steps for Gauss elimination.

For a review, go to:

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

You should eliminate variables systematically.

 

[Denis]

x - y + 5z = -9 [1]
5x + z = -1 [2]
x + 4y + z =15 [3]

As Subhotosh told you: you should eliminate variables systematically.

Plus "number" the equations (as I've shown), in order to be CLEARER.

And a bit of thinking can help a lot; like, did you notice there is no y term in [2]?
So next logical step is eliminate y from [1] + [3].