Question

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

Answer 1

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

Explanation:

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