Question 932411

{{{-4x-8y-z=-64}}}.....eq.1
{{{x+2y+7z=43}}}.....eq.2
{{{-8x+y+z=-65}}}.....eq.3
___________________________

start with
{{{-4x-8y-z=-64}}}.....eq.1
{{{-8x+y+z=-65}}}.....eq.3
_____________________________add both

{{{-4x-8y-z-8x+y+z=-64-65}}}


{{{-12x-7y-cross(z)+cross(z)=-129}}}

{{{-12x-7y=-129}}}....solve for {{{y}}}

{{{-12x+129=7y}}}

{{{-(12/7)x+129/7=y}}}

{{{-(12/7)x+129/7=y}}}

{{{y=-1.71x+18.43}}}.........1a

go to {{{x+2y+7z=43}}}.....eq.2, substitute {{{y}}} and solve for {{{x}}}


{{{x+2(-1.71x+18.43)+7z=43}}}


{{{x-3.42x+36.86+7z=43}}}

{{{-2.42x=-7z+43-36.86}}}

{{{-2.42x=-7z+6.14}}}

{{{2.42x=7z-6.14}}}

{{{x=7z/2.42-6.14/2.42}}}

{{{x=-2.89z-2.54}}}.........1b


{{{-4(-2.89z-2.54)-8(-1.71x+18.43)-z=-64}}}.....eq.1

{{{11.56z+10.16+13.68(-2.89z-2.54)-147.44-z=-64}}}

{{{11.56z+10.16-39.54z-34.75-147.44-z=-64}}}

{{{-28.98z-172.03=-64}}}

{{{-28.98z=172.03-64}}}

{{{-28.98z=108.03}}}

{{{z=108.03/-28.98}}}

{{{highlight(z=-3.73)}}}

go to
{{{x=-2.89(-3.73)-2.54}}}.........1b

{{{x=10.7797-2.54}}}

{{{highlight(x=8.24)}}}



{{{y=-1.71*8.24+18.43}}}.........1a

{{{y=-14.09+18.43}}}

{{{highlight(y=4.34)}}}


{{{-4*8.24-8*4.34-(-3.73)=-64}}}.....eq.1

{{{-32.96-34.72+3.73=-64}}}

{{{-63.95=-64}}}...round it to whole number

{{{-64=-64}}}