Question 767482


{{{(1/3)x - (1/4)y + z = -9}}}.........eq.1.....multiply by {{{12}}}
{{{(1/2)x - (1/3)y - (1/4)z = -6}}}....eq.2....multiply by {{{12}}}
{{{x - (1/2)y - z = -8}}}..............eq.3....multiply by {{{2}}}
_________________________________________

{{{12(1/3)x - 12(1/4)y + 12z = -9*12}}}.........eq.1
{{{12(1/2)x - 12(1/3)y - 12(1/4)z = -6*12}}}....eq.2
{{{2x - 2(1/2)y - 2z = -8*2}}}..............eq.3
__________________________________________________

{{{4x - 3y + 12z = -108}}}.........eq.1
{{{6x - 4y - 3z = -72}}}....eq.2
{{{2x - y - 2z = -16}}}..............eq.3
______________________________________

{{{6x - 4y - 3z = -72}}}....eq.2
{{{2x - y - 2z = -16}}}..............eq.3....multiply by {{{3}}} 
______________________________________

{{{6x - 4y - 3z = -72}}}....eq.2
{{{6x - 3y - 6z = -48}}}..............eq.3......subtract eq.3 from eq.2
_______________________________

{{{6x-6x - 4y-(-3y) - 3z-(-6z) = -72-(-48)}}}

{{{- 4y+3y - 3z+6z = -72+48}}}

{{{-y+3z = -24}}}.....solve for {{{y}}}

{{{24+3z = y}}}.....plug in eq.1


{{{4x - 3(24+3z) + 12z = -108}}}.........eq.1

{{{4x - 72-9z + 12z = -108}}}

{{{4x  + 3z = -108+72}}}

{{{4x  + 3z = -36}}}......solve for {{{x}}}

{{{ 4x= -3z-36}}}

{{{ x = -(3/4)z-9}}}.........go to eq.3 and plug in {{{y}}} and {{{x}}}

{{{2x - y - 2z = -16}}}..............eq.3.

{{{2(-(3/4)z-9) - (24+3z )- 2z = -16}}} ....solve for {{{z}}}

{{{-(3/2)z-18 - 24-3z - 2z = -16}}}...all terms multiply by {{{2}}}

{{{-2(3/2)z-18*2 - 24*2-5*2z = -16*2}}}

{{{-3z-36- 48-10z = -32}}}

{{{32-36- 48 = 3z+10z}}}

{{{32-84 =13z}}}

{{{-52 =13z}}}

{{{-52/13=z}}}

{{{highlight(z=-4)}}}..........now we can find {{{x}}} and {{{y}}}


{{{ x = -(3/4)z-9}}}=>{{{ x = -(3/4)(-4)-9}}} =>{{{ x = 3-9}}}=>{{{ highlight(x = -6)}}}

{{{y=24+3z }}}=>{{{y=24+3(-4) }}}=>{{{y=24-12 }}}=>{{{highlight(y=12) }}}