# Thread: Gaussian elimination to solve systems:

1. ## Gaussian elimination to solve systems:

Use Gaussian elimination to solve the systems:
2x + 3y - z = 4
4x - 2y + 3z = -7
-6x + 7y - 7z = 3
x = -7.5
y= 9.3
z= 8.9
Im a little stumped, the answer i got for x y and z when plugged in, do not work and are incorrect. I would post my work (around 5 or 6 steps) but I trashed it after finding out it was wrong therefore losing it..
Would anyone be willing to show me step for step how to solve this problem?
thanks so much!!

2. Are you sure you typed that correctly? I couldn't solve it and when I entered it into my calculator it said there were no solutions.

3. Originally Posted by Murphie
Use Gaussian elimination to solve the systems:
2x + 3y - z = 4
4x - 2y + 3z = -7
-6x + 7y - 7z = 3
Unfortunately, since you did not show your work, it is not possible to help you find where you might have gone wrong. Sorry!

There are any number of ways to approach this. Since the determinant is zero, obviously this will not have a unique solution. The only remaining question is whether there is an infinite solution (with a row of the reduced-row echelon form being all zeroes) or no solution (with a row being nonsense, like 0x + 0y + 0z = 12).

To find out, we do row operations. There are any number of ways to proceed. The following is one:

[html] 2x + 3y - z = 4
4x - 2y + 3z = -7
-6x + 7y - 7z = 3

-2R1 + R2 -> R2
3R1 + R3 -> R3

2x + 3y - z = 4
- 8y + 5z = -15
16y - 10z = 15

2R2 + R3 -> R3

2x + 3y - z = 4
- 8y + 5z = -15
0 = -15[/html]
What does this tell you?