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

Answer:

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#