Question 1134299


{{{x+2y-3z=-7}}}
{{{2x-3y+z=14}}}
{{{4x+y-2z=3}}}


the system in matrix form:


{{{matrix(3,4,1,	2,	-3,	-7,
2,	-3,	1,	14,
4,	1,	-2,	3)}}}


multiply {{{1}}} row by {{{2}}} and subtract it from {{{2}}} row, and multiply {{{1}}} row by {{{4}}} and subtract it from {{{3}}} row


{{{matrix(3,4,1,	2,	-3,	-7,
0,	-7,	7,	28,
0,	-7,	10,	31)}}}



divide the {{{2}}} row by {{{-7}}}


{{{matrix(3,4,1,	2,	-3,	-7,
0,	1,	-1,	-4,
0,	-7,	10,	31)}}}


multiply {{{2}}} row by {{{2}}} and subtract it from {{{1}}} row, and multiply {{{2 }}}row by {{{7 }}}and add it to {{{3}}} row


{{{matrix(3,4,1,	0,	-1,	1,
0,	1,	-1,	-4,
0,	0,	3,	3)}}}


divide the {{{3}}} row by {{{3}}}


{{{matrix(3,4,1,	0,	-1,	1,
0,	1,	-1,	-4,
0,	0,	1,	1)}}}


multiply {{{3}}} row by {{{1}}} and add it to {{{1}}} row, and multiply {{{3}}} row by {{{1 }}}and add it to {{{2}}} row


{{{matrix(3,4,1,	0,	0,	2,
0,	1,	0,	-3,
0,	0,	1,	1)}}}


solutions:

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