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

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Answer 1 · 2016-01-19T14:15:05

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

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

How do you solve using gaussian elimination or gauss-jordan elimination, 3x + y + 2z = 33x + y + 2z = 3, 2x - 37 - z = -32x - 37 - z = -3, x + 2y + z = 4x + 2y + z = 4?