Question 1152642

{{{3x-4z=-1}}}...........1
{{{2y+3z=2}}}...........2
{{{2x+3y=6}}}...........3
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{{{3x-4z=-1}}}......solve for {{{z}}}

{{{3x+1=4z}}}

{{{z=(3x+1)/4}}}...........1a

{{{2y+3z=2}}}.....solve for {{{z}}}

{{{z=2(1-y)/3}}}..........2a


from 1a and 2a we have


{{{(3x+1)/4=2(1-y)/3}}}.....solve for {{{x}}}

{{{(3x+1)/4=2(1-y)/3}}}.........cross multiply

{{{3(3x+1)=4*2(1-y)}}}

{{{9x+3=8-8y}}}....solve for {{{x}}}

{{{9x=8-8y-3}}}

{{{9x=5-8y}}}

{{{x=(5-8y)/9}}}.........3a


{{{2x+3y=6}}}.........3, substitute{{{ x}}}

{{{2(5-8y)/9+3y=6}}}....solve for {{{y}}}

{{{2(5-8y)+9*3y=6*9}}}

{{{10-16y+27y=54}}}

{{{11y=54-10}}}

{{{11y=44}}}

{{{y=4}}}

go to

{{{x=(5-8y)/9}}}.........3a, plug in {{{y}}}

{{{x=(5-8*4)/9}}}

{{{x=(5-32)/9}}}

{{{x= -27/9}}}

{{{x= -3}}}

go to

{{{z=(3x+1)/4}}}...........1a, plug in {{{x}}}

{{{z=(3(-3)+1)/4}}}

{{{z=(-9+1)/4}}}

{{{z=-8/4}}}

{{{z=-2}}}

solutions:

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