How do you solve using gaussian elimination or gauss-jordan elimination, $3 x - 10 y = - 25$ $3x - 10y = -25$ , $4 x + 40 y = 20$ $4x + 40y = 20$ ?

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Answer 1 · 2017-07-07T09:36:05

$color(brown)(((1,0,|,-5),(0,1,|,1)))color(blue)(=>((" "x=-5),(" "y=+1))$

Given:
$3x-10y=-25$
$4x+40y=20$

Using the requested method.

$[(color(white)(.)x," "y,|,color(white)(.)c color(white)(..))]$

$color(brown)(((3,-10,|,-25),(4,40,|,20)))$
$" "R_1xx4andR_2xx3$
$" "darr$

$color(brown)(((12,-40,|,-100),(12,120,|,60)))$
$" "R_2 - R_1$
$" "darr$

$color(brown)(((12,-40,|,-100),(0,160,|,160)))$
$" "R_2 -:160$
$" "darr$

$color(brown)(((12,-40,|,-100),(0,1,|,1)))color(blue)( =>y=1)$
$" "R_1 -:12$
$" "darr$

$color(brown)(((1,-10/3,|,-25/3),(0,1,|,1)))$
$" "R_1 +10/3R_2$
$" "darr$

$color(brown)(((1,0,|,-5),(0,1,|,1)))color(blue)(=>x=-5)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check:
$3x-10y" "->" "3(-5)-10(1)" "->" "-15-10=-25$

Required solution is -25 so the values are correct

How do you solve using gaussian elimination or gauss-jordan elimination, 3x - 10y = -253x−10y=−253x - 10y = -25, 4x + 40y = 204x+40y=204x + 40y = 20?