Question

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

Answer 1

See Gaussian elimination for a very good explanation

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

Explanation:

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

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