Question 1134300

{{{-4x - 3y - z = -36}}}
{{{x + 7y - 9z = -68}}}
{{{8x + y + z = 58}}}


Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination)


{{{matrix(3,4,-4,	-3,	-1,	-36,
1,	7,	-9,	-68,
8,	1,	1,	58)}}}



divide the {{{1}}} row by {{{-4}}}


{{{matrix(3,4,1,	0.75,	0.25,	9,
1,	7,	-9,	-68,
8,	1,	1,	58)}}}


multiply {{{1}}} row by {{{1}}} and subtract it from {{{2}}} row, and multiply {{{1}}} row by {{{8 }}}and subtract it from {{{3}}} row


{{{matrix(3,4,1,	0.75,	0.25,	9,
0,	6.25,	-9.25,	-77,
0,	-5,	-1,	-14)}}}


divide the {{{2}}} row by{{{ 6.25}}}


{{{matrix(3,4,1,	0.75,	0.25,	9,
0,	1,	-1.48,	-12.32,
0,	-5,	-1,	-14)}}}



multiply {{{2}}} row by {{{0.75}}} and subtract it from {{{1}}} row, and multiply {{{2}}} row by {{{5}}} and add it to {{{3}}} row



{{{matrix(3,4,1,	0,	1.36,	18.24,
0,	1,	-1.48,	-12.32,
0,	0,	-8.4,	-75.6)}}}



divide the {{{3}}} row by {{{-8.4}}}


{{{matrix(3,4,1,	0,	1.36,	18.24,
0,	1,	-1.48,	-12.32,
0,	0,	1,	9)}}}



multiply {{{3}}} row by {{{1.36}}} and subtract it from {{{1}}} row, and multiply {{{3 }}}row by {{{1.48 }}}and add it to{{{ 2}}} row



{{{matrix(3,4,1,	0,	0,	6,
0,	1,	0,	1,
0,	0,	1,	9)}}}


solutions:

{{{x = 6}}}
{{{y = 1}}}
{{{z= 9}}}