Question 1114851
Your matrix:

{{{matrix(4,5,1,	3,	-1,	2,	-15,
2,	7,	2,	-4,	27,
-3,	-8,	3,	4,	-10,
4,	11,	-2,	-3,	35)}}}


Find the pivot in the 1st column in the 1st row:


{{{matrix(4,5,
highlight(1),	3,	-1,	2,	-15,
2,	7,	2,	-4,	27,
-3,	-8,	3,	4,	-10,
4,	11,	-2,	-3,	35)}}}



Eliminate the 1st column:


{{{matrix(4,5,
1,	3,	-1,	2,	-15,
0,	1,	4,	-8,	57,
0,	1,	0,	10,	-55,
0,	-1,	2,	-11,	95)}}}


Find the pivot in the 2nd column in the 2nd row:


{{{matrix(4,5,
1,	3,	-1,	2,	-15,
0,	highlight(1),	4,	-8,	57,
0,	1,	0,	10,	-55,
0,	-1,	2,	-11,	95)}}}


Eliminate the 2nd column:

{{{matrix(4,5,
1,	0,	-13,	26,	-186,
0,	1,	4,	-8,	57,
0,	0,	-4,	18,	-112,
0,	0,	6,	-19,	152)}}}



Make the pivot in the 3rd column by dividing the 3rd row by {{{-4}}}:

{{{matrix(4,5,
1,	0,	-13,	26,	-186,
0,	1,	4,	-8,	57,
0,	0,	1,	-9/2,	28,
0,	0,	6,	-19,	152)}}}


Eliminate the 3rd column:


{{{matrix(4,5,
1,	0,	0,	-65/2,	178,
0,	1,	0,	10,	-55,
0,	0,	1,	-9/2,	28,
0,	0,	0,	8,	-16)}}}


Make the pivot in the 4th column by dividing the 4th row by {{{8}}}:

{{{matrix(4,5,
1,	0,	0,	-65/2,	178,
0,	1,	0,	10,	-55,
0,	0,	1,	-9/2,	28,
0,	0,	0,	1,	-2)}}}


Eliminate the 4th column:


{{{matrix(4,5,
1,	0,	0,	0,	113,
0,	1,	0,	0,	-35,
0,	0,	1,	0,	19,
0,	0,	0,	1,	-2)}}}



Solution set:

({{{113}}},{{{ -35}}}, {{{19}}}, {{{-2}}})