Question 828221
Algebra.com does not display matrices well. So I am just going to show you the rectangular array of numbers without the usual brackets.
<pre>
Initial matrix:
     2     2     3    -6
     3     5     4     3
     2     3     4   -10
Replace row 1 with 1/2 times row 1:
     1     1   3/2    -3
     3     5     4     3
     2     3     4   -10
Add -3 times row 1 to row 2:
      1      1    3/2     -3
      0      2   -1/2     12
      2      3      4    -10
Add -2 times row 1 to row 3:
      1      1    3/2     -3
      0      2   -1/2     12
      0      1      1     -4
Replace row 2 with 1/2 times row 2:
      1      1    3/2     -3
      0      1   -1/4      6
      0      1      1     -4
Add -1 times row 2 to row 1:
      1      0    7/4     -9
      0      1   -1/4      6
      0      1      1     -4
Add -1 times row 2 to row 3:
      1      0    7/4     -9
      0      1   -1/4      6
      0      0    5/4    -10
Replace row 3 with 4/5 times row 3:
      1      0    7/4     -9
      0      1   -1/4      6
      0      0      1     -8
Add -7/4 times row 3 to row 1:
      1      0      0      5
      0      1   -1/4      6
      0      0      1     -8
Add 1/4 times row 3 to row 2:
    1    0    0    5
    0    1    0    4
    0    0    1   -8
which translates back into:
x = 5
y = 4
z = -8