Gaussian Elimination means that the augmented matrix should be reduced to a triangular matrix, and then use reverse substitutions to solve. The matrices look like this:

[1 1 1 9]

[1 -2 3 8]

[2 1 -1 3], then

[1 1 1 9]

[0 -3 2 -1]

[0 -1 -3 -15], then

[1 1 1 9]

[0 1 3 15]

[0 -3 2 -1], then

[1 1 1 9]

[0 1 3 15]

[0 0 11 44].

The last row stands for the equation 11z = 44, so z = 4.

The second row stands for the equation y + 3z = 15, so y + 3(4) = 15, and y = 3.

The first row stands for x + y + z = 9, so x + 3 + 4 = 9, and x = 2.

[1 1 1 9]

[1 -2 3 8]

[2 1 -1 3], then

[1 1 1 9]

[0 -3 2 -1]

[0 -1 -3 -15], then

[1 1 1 9]

[0 1 3 15]

[0 -3 2 -1], then

[1 1 1 9]

[0 1 3 15]

[0 0 11 44].

The last row stands for the equation 11z = 44, so z = 4.

The second row stands for the equation y + 3z = 15, so y + 3(4) = 15, and y = 3.

The first row stands for x + y + z = 9, so x + 3 + 4 = 9, and x = 2.