Question 121110
{{{ 2x + y - 3z = 0}}}……………….(1)….=> {{{y= - 2x + 3z}}} ……… (I)
 
{{{-2x + 2y + z  = -7}}}……………..(2)….=> {{{z =2x - 2y -7}}}……………(II)

{{{ x - 4y - 3z  = 7}}}………………..(3)


From (I) and (II) we have:

{{{y = -2x + 3z}}}…….(I)……….substitute {{{z}}} from (II)

{{{y = -2x + 3z}}}…….(
{{{y = -2x + 3(2x - 2y -7)}}}…….

{{{y = -2x + 6x- 6y -21)}}}…….

{{{y = 4x- 6y -21)}}}…….

{{{y +6y = 4x-21)}}}…….

{{{7y = 4x - 21 }}}

{{{y = (4/7)x - 3}}}……………………(III)




{{{ x - 4y - 3z = 7}}}………………..(3)………..substitute {{{y}}} from (III)


{{{ x - 4((4/7)x - 3) - 3z = 7}}}………………..substitute {{{z}}} from (II)


{{{ x - 4((4/7)x - 3) - 3(2x - 2y -7) = 7}}}………………..substitute {{{y}}} from (III)

{{{ x - 4((4/7)x - 3) - 3(2x - 2((4/7)x - 3) -7) = 7}}}………………..


{{{ x - ((16/7)x - 12) - (6x - (24/7)x - 18) -21) = 7}}}………………..solve for {{{x}}}


{{{ x -(16/7)x + 12 - 6x + (24/7)x -18 + 21 = 7}}}………………..


{{{ -(16/7)x - 5x + (24/7)x + 15 = 7}}}……………….

{{{  - 5x + (8/7)x + 15 = 7}}}………………..

{{{  - 5x + (8/7)x = 7 - 15}}}………………..

{{{  - 5x + (8/7)x = - 8}}}………………..multiply both sides by {{{7}}}


{{{  - 35x + 8x = - 56}}}………………..


{{{  - 27x = - 56}}}………………..


{{{  x = - 56/-27}}}………………..

{{{x = 2.07}}}





{{{y = (4/7)x - 3}}}………...................(III)

{{{y = (4/7)( 0.52) – 3 }}}……

{{{y = (0.57)( 2.07) - 3}}}……

{{{y = 1.1799 - 3}}}

{{{y = -1.8201}}}

{{{y = -1.8}}}



{{{z = 2(2.07) – 2(-1.8) -7}}}………… (II)

{{{z = 4.14 + 3.6 - 7 }}}…………

{{{z = 7.74 - 7}}}…………

{{{z = 0.74}}}…………


Check:

{{{ 2x + y - 3z = 0}}}……………….(1)….=>

{{{ 2(2.07)  -1.8 – 3 (0.74) = 0}}}……………….

{{{ 4.14 - 1.8 - 2.22 = 0}}}……………….

{{{ 4.14 - 4.02 = 0}}}……………….

{{{ 4 - 4 = 0}}}……………….

{{{ 0 = 0}}}……………….


Check second and third one too………………