Question 906681
{{{2x + 3y- z= -16}}} ............1
{{{x + 2y + 2z= -3}}} ............2
{{{-3x + y + z= -5}}} .............3
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{{{2x + 3y- z= -16}}} ............1
{{{x + 2y + 2z= -3}}} ............2..multiply by {{{-2}}} 
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{{{2x + 3y- z= -16 }}}............1
{{{-2x + 2(-2)y + 2(-2)z= -3(-2)}}} ............2
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{{{2x + 3y- z= -16 }}}............1
{{{-2x -4y -4z= 6}}} ............2.....add both
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{{{2x + 3y- z -2x -4y -4z= -16+6}}}
{{{ -y -5z= -10}}}
{{{10 -5z= y}}}................1a

now take these two:

{{{x + 2y + 2z= -3}}} ............2....multiply by {{{3}}}
{{{-3x + y + z= -5}}} .............3
____________________.and add

{{{3x + 6y + 6z+(-3x + y + z)= -9-5}}}

{{{3x + 6y + 6z-3x + y + z= -14}}}

{{{ 7y + 7z  = -14}}}

{{{7(y + z ) = -14}}}

{{{(y + z ) = -14/7}}}
{{{y + z = -2}}}
{{{y  = -2-z}}}............1b


use 1a and 1b to calculate {{{z}}}

{{{10 -5z= y}}}................1a
{{{ -2-z=y}}}............1b
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=>

{{{10 -5z=-2-z}}}
{{{10 +2=5z-z}}}
{{{12=4z}}}
{{{highlight(z=3)}}}

now find {{{y}}}

 {{{-2-z=y}}}
{{{ -2-3=y}}}
 {{{highlight(y=-5)}}}

and, find {{{x}}}

{{{x + 2y + 2z= -3}}} ............2
{{{x + 2(-5) + 2*3= -3}}} 
{{{x -10 + 6= -3}}} 
{{{x -4= -3 }}}
{{{x = -3 +4}}}
{{{highlight(x = 1)}}}