SOLUTION: Alright, I do my homework on my math lab and it has an option called "show me how." This is the problem, Use the Gauss-Jordan method if the system has infinitely many solutions, gi

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Question 378575: Alright, I do my homework on my math lab and it has an option called "show me how." This is the problem, Use the Gauss-Jordan method if the system has infinitely many solutions, give the solutions, z arbitrary.
x-5y+4z+1
3x-2y+3z=-2
Now i get down to here(just imagine there are brackets around these because i'm not able to put them in but they are matrices).
1 -5 4 | 1
0 1 -9/13 |-5/13
now i'm confused on what to do from here, i understand that i need to turn the -5 in to a 0 but the computer keeps telling me i'm wrong. so please don't skip any steps whatsoever.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Add 5 times the second row to the first to get the new matrix 


1              0        7/13     | -12/13
0              1       -9/13     | -5/13


Now the matrix is in reduced row echelon form (ie we can't do any more steps)


So the first line means that . Multiply EVERY term by the LCD 13 to get and then solve for 'x' to get


The second line means that . Multiply EVERY term by the LCD 13 to get and then solve for 'y' to get


So the solution as an ordered triple is in the form


where 'z' is any arbitrary real number.


Because 'z' can be any real number, this means that the system has an infinite number of solutions.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim