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

1 Answer
Jan 15, 2016

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