Question 1152439

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


start with


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

{{{x=y-2z-4}}}............3a

then,

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

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

{{{x=2z-3y/2+2}}}.........2a


from 2a and 3a we have


{{{y-2z-4=2z-3y/2+2}}}.......solve for {{{y}}}

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

{{{5y/2=4z+6}}}

{{{5y=8z+12}}}

{{{y=8z/5+12/5}}}................2b

go to 

{{{x=y-2z-4}}}............3a, substitute {{{y}}}

{{{x=8z/5+12/5-2z-4}}}

{{{x=8z/5+12/5-10z/5-20/5}}}

{{{x=-2z/5-8/5}}}...........3b


go to

{{{3x+y-4z=-6}}}..........1...substitute {{{x}}} and {{{y}}}, and solve for{{{ z}}}

{{{3(-2z/5-8/5)+(8z/5+12/5)-4z=-6}}}

{{{-6z/5-24/5+8z/5+12/5-20z/5=-6}}}

{{{-(18 z)/5 - 12/5 = -6}}}

{{{6 - 12/5 = (18 z)/5}}}

{{{(18 z)/5=30/2-12/5

{{{(18 /5)z=18/5}}}

{{{z=1}}}




go to 

{{{x=-2z/5-8/5}}}...........3b.....substitute {{{z}}}

{{{x=-(2*1)/5-8/5}}}...........3b

{{{x=-2/5-8/5 }}}

{{{x=-10/5 }}}

{{{x=-2}}}

go to

{{{y=8z/5+12/5}}}................2b...substitute {{{z}}}

{{{y=(8*1)/5+12/5}}}

{{{y=8/5+12/5}}}

{{{y=20/5}}}

{{{y=4}}}

solutions:

{{{x = -2 }}}
{{{y = 4 }}}
{{{z = 1}}}