Question 922594


{{{3x+4y+z=7}}}......eq.1
{{{2y+z=3}}}.........eq.2
{{{-5x+3y+8z=-31}}}......eq.3
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{{{ 2y+z=3}}}......eq.2 ...solve for {{{z}}}

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


{{{3x+4y+z=7}}}......eq.1...plug in {{{z}}}

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

{{{3x+2y=7-3}}}

{{{3x+2y=4}}}......solve for {{{x}}}

{{{3x=4-2y}}}

{{{x=4/3-2y/3}}}


{{{-5x+3y+8z=-31}}}......eq.3..plug in {{{z}}} and {{{x}}}

{{{-5(4/3-2y/3)+3y+8(3- 2y)=-31}}}...solve for {{{y}}}

{{{-20/3+10y/3+3y+24- 16y=-31}}}...both sides multiply by {{{3}}}

{{{-20+10y+9y+72- 48y=-93}}}

{{{19y-48y=-93+20-72}}}

{{{-29y=-145}}}.....both sides multiply by {{{-1}}}


{{{29y=145}}}

{{{y=145/29}}}

{{{highlight(y=5)}}}

go to {{{z=3- 2y}}} plug in {{{y}}}


{{{z=3- 2*5}}}

{{{z=3- 10}}}

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

go to {{{x=4/3-2y/3}}} plug in {{{y}}}

{{{x=4/3-(2*5)/3}}}

{{{x=4/3-10/3}}}

{{{x=-6/3}}}

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


so, {{{highlight(x=-2)}}}, {{{highlight(y=5)}}}, and {{{highlight(z=-7)}}}


check: 

{{{3x+4y+z=7}}}......eq.1

{{{3(-2)+4*5+(-7)=7}}} 

{{{-6+20-7=7}}}

{{{20-13=7}}}

{{{7=7}}}