How do you solve using gaussian elimination or gauss-jordan elimination, #3x + y + 2z = 3#, #2x - 37 - z = -3#, #x + 2y + z = 4#?

1 Answer
Jan 19, 2016

Answer:

#x = 617/276#
#y = -15/92#
#z = 577/276#

Explanation:

I assume that there is a transcription error in the question and the second term in the second equation should actually be a #y# term.

#3x + y + 2z = 3#
#2x - 37y - z = -3#
#x+2y+z = 4#

Adding together the second and third equations gives us
#3x -35y =1#

Next, doubling the second equation and adding it to the first gives
#7x -73y = -3#

Solving these two equations gives #7*(3+35y)/3 -73y = -3#
#21+35y - 219y -= - 9#
#184y = -30#
#y = -15/92#

#:.3x = 1+35*15/92 = (92+525)/92 = 617/92#
#x = 617/276#

Then #z = 4 - 617/276 -2*(-15/92)#
#z = (1104 - 617 +90)/276 = 577/276#