Question 939300
Result of solution using Gauss-Jordan elimination

Your matrix
	x	y	z	b
-3	2	-6	6
5	7	-5	6
1	4	-2	8




Find the pivot in the 1st column and swap the 3rd and the 1st rows
x	y	z	b
1	4	-2	8
5	7	-5	6
-3	2	-6	6



Multiply the 1st row by 5
x	y	z	b
5	20	-10	40
5	7	-5	6
-3	2	-6	6



Subtract the 1st row from the 2nd row and restore it
x	y	z	b
1	4	-2	8
0	-13	5	-34
-3	2	-6	6


Multiply the 1st row by -3
x	y	z	b
-3	-12	6	-24
0	-13	5	-34
-3	2	-6	6


Subtract the 1st row from the 3rd row and restore it
	x	y	z	b
1	4	-2	8
0	-13	5	-34
0	14	-12	30


Make the pivot in the 2nd column by dividing the 2nd row by -13
	x	y	z	b
1	4	-2	8
0	1	-5/13	34/13
0	14	-12	30


Multiply the 2nd row by 4
	x	y	z	b
1	4	-2	8
0	4	-20/13	136/13
0	14	-12	30


Subtract the 2nd row from the 1st row and restore it
	x	y	z	b
1	0	-6/13	-32/13
0	1	-5/13	34/13
0	14	-12	30



Multiply the 2nd row by 14
	x	y	z	b
1	0	-6/13	-32/13
0	14	-70/13	476/13
0	14	-12	30



Subtract the 2nd row from the 3rd row and restore it
x	y	z	b
1	0	-6/13	-32/13
0	1	-5/13	34/13
0	0	-86/13	-86/13


Make the pivot in the 3rd column by dividing the 3rd row by -86/13
	x	y	z	b
1	0	-6/13	-32/13
0	1	-5/13	34/13
0	0	1	1


Multiply the 3rd row by -6/13
x	y	z	b
1	0	-6/13	-32/13
0	1	-5/13	34/13
0	0	-6/13	-6/13


Subtract the 3rd row from the 1st row and restore it
x	y	z	b
1	0	0	-2
0	1	-5/13	34/13
0	0	1	1



Multiply the 3rd row by -5/13
	x	y	z	b
1	0	0	-2
0	1	-5/13	34/13
0	0	-5/13	-5/13


Subtract the 3rd row from the 2nd row and restore it
	x	y	z	b
1	0	0	-2
0	1	0	3
0	0	1	1


Solution set:

{{{x = -2}}}
{{{y = 3}}}
{{{z = 1}}}