What is the Gauss-jordan method?

Question

Use the​ Gauss-Jordan method to solve the system of equations. If the system has infinitely many​ solutions, give the solution with z arbitrary.

4x+2y-3z+6=0

2x-y+2z-6=0

-8x-4y+6z=0

Answer 1

4x + 2y - 3z = -6

2x - y + 2z = 6

-8x - 4y + 6z = 0

Switch equation 1 and equation 2:

2x - y + 2z = 6

4x + 2y - 3z = -6

-8x - 4y + 6z = 0

Multiply equation 1 by -2 and add to equation 2

Multiply equation 1 by 4 and add to equation 3:

2x - y + 2z = 6

4y - 7z = -18

-8y + 14z = 24

Multiply equation 2 by 2 and add to equation 3:

2x - y + 2z = 6

4y - 7z = -18

0 = -12 NO SOLUTION