Question 753656
{{{2x-4y-z=17}}}...eq.1
{{{x+2y-z=0}}}...eq.2
{{{4x-y-z=6}}}...eq.3
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{{{x+2y-z=0}}}...eq.2..solve for {{{x}}}


{{{x=z-2y}}}...eq.2a.......substitute in .eq.1


{{{2(z-2y)-4y-z=17}}}...eq.1

{{{2z-4y-4y-z=17}}}

{{{z-8y=17}}}....solve for {{{z}}}

{{{z=17+8y}}}....eq.1a

go to {{{x=z-2y}}}...eq.2a and substitute {{{z}}}

{{{x=17+8y-2y}}}

{{{x=17+6y}}}........eq.2b

go to {{{4x-y-z=6}}}...eq.3 and substitute {{{z}}} from eq.1a and {{{x}}} from eq.2b

{{{4(17+6y)-y-(17+8y)=6}}}.....solve for {{{y}}}

{{{68+24y-y-17-8y=6}}}

{{{51+24y-9y=6}}}

{{{15y=6-51}}}

{{{15y=-45}}}

{{{y=-45/15}}}

{{{highlight(y=-3)}}}

go back to {{{x=17+6y}}}........eq.2b and find {{{x}}}

{{{x=17+6*(-3)}}}

{{{x=17-18}}}

{{{highlight(x=-1)}}}

go back to {{{z=17+8y}}}....eq.1a and find {{{z}}}

{{{z=17+8(-3)}}}

{{{z=17+-24}}}

{{{highlight(z=-7)}}}


check:

{{{x+2y-z=0}}}...eq.2..plug in {{{highlight(x=-1)}}},{{{highlight(y=-3)}}}, and {{{highlight(z=-7)}}}

{{{-1+2(-3)-(-7)=0}}}

{{{-1-6+7=0}}}

{{{-7+7=0}}}

{{{0=0}}} which confirms our solutions