How do you solve using gaussian elimination or gauss-jordan elimination, $2 x + 4 y - 6 z = 48$ $2x+4y-6z=48$ , $x + 2 y + 3 z = - 6$ $x+2y+3z=-6$ , $3 x - 4 y + 4 z = - 23$ $3x-4y+4z=-23$ ?

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How do you solve using gaussian elimination or gauss-jordan elimination, $2 x + 4 y - 6 z = 48$ $2x+4y-6z=48$ , $x + 2 y + 3 z = - 6$ $x+2y+3z=-6$ , $3 x - 4 y + 4 z = - 23$ $3x-4y+4z=-23$ ?

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Answer 1 · 2016-01-15T09:41:02

See Gaussian elimination for a very good explanation

$x = 3$ $x=3$ , $y = 3$ $y=3$ and $z = - 5$ $z=-5$

Explanation:

$2 x + 4 y - 6 z = 48$ $2x+4y-6z=48$
$x + 2 y + 3 z = - 6$ $x+2y+3z=-6$
$3 x - 4 y + 4 z = - 23$ $3x-4y+4z=-23$

Adding the first and third equations gives $5 x - 2 z = 25$ $5x-2z=25$
Doubling the second equation and adding it to the third gives $5 x + 10 z = - 35$ $5x+10z =-35$
We can now use these two equations to solve for $z$ $z$ subtracting one from the other gives $- 12 z = 60$ $-12z = 60$
$:. z = -5$

$:.5x - 2(-5) = 25$
$5x = 15$
$x=3$

Returning to the original second equation:
$3 +2y +3(-5) = -6$
$2y = -6 -3 +15$
$y = 3$

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How do you solve using gaussian elimination or gauss-jordan elimination, $2 x + 4 y - 6 z = 48$ $2x+4y-6z=48$ , $x + 2 y + 3 z = - 6$ $x+2y+3z=-6$ , $3 x - 4 y + 4 z = - 23$ $3x-4y+4z=-23$ ?

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Explanation:

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How do you solve using gaussian elimination or gauss-jordan elimination, 2x+4y-6z=482x+4y−6z=482x+4y-6z=48, x+2y+3z=-6x+2y+3z=−6x+2y+3z=-6, 3x-4y+4z=-233x−4y+4z=−233x-4y+4z=-23?

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Explanation:

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How do you solve using gaussian elimination or gauss-jordan elimination, $2 x + 4 y - 6 z = 48$ $2x+4y-6z=48$ , $x + 2 y + 3 z = - 6$ $x+2y+3z=-6$ , $3 x - 4 y + 4 z = - 23$ $3x-4y+4z=-23$ ?