Question 477998

{{{2x-3y+z=13}}}.....1

{{{x+2y+3z=2}}}.......2

{{{3x-y+z=12}}}.......3
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{{{2x-3y+z=13}}}.....1...solve for {{{z}}}

{{{z=-2x+3y+13}}}..........plug in 3

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{{{3x-y+(-2x+3y+13)=12}}}.......3

{{{3x-y-2x+3y+13=12}}}

{{{x+2y=12-13}}}

{{{x+2y=-1}}}............solve for {{{x}}}

{{{x=-2y-1}}}.
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{{{z=-2x+3y+13}}}...plug in {{{x}}}

{{{z=-2(-2y-1)+3y+13}}}

{{{z=4y+2+3y+13}}}

{{{z=7y+15}}}....plug in 2 along with {{{x=-2y-1}}}

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{{{x+2y+3z=2}}}....2

{{{(-2y-1)+2y+3(7y+15)=2}}}

{{{-2y-1+2y+21y+45=2}}}

{{{21y+44=2}}}

{{{21y=2-44}}}

{{{21y=-42}}}

{{{y=-42/21}}}


{{{y=-2}}}.............the solution .....plug in {{{x=-2y-1}}}

{{{x=-2(-2)-1}}}

{{{x=4-1}}}

{{{x=3}}}...........the solution


now find {{{z}}}

{{{z=7y+15}}}

{{{z=7(-2)+15}}}

{{{z=-14+15}}}

{{{z=1}}}..........the solution


so, solutions are:

{{{x=3}}}

{{{y=-2}}} and

{{{z=1}}}

check:


{{{2x-3y+z=13}}}.....1

{{{2(3)-3(-2)+1=13}}}

{{{6+6+1=13}}}

{{{13=13}}}