Question 417787


{{{x+y+z=-9}}} ..............1

{{{2x+4y+2z=-14}}}...........2 

{{{-x+6y-32=35}}}.............3..... find solution

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{{{x+y+z=-9}}} ..............1.solve for {{{x}}}

{{{x=-9-y-z}}}.........plug in 2

{{{2x+4y+2z=-14}}}...........2 

{{{2(-9-y-z)+4y+2z=-14}}}

{{{-18-2y-2z+4y+2z=-14}}}

{{{cross(-2z)+2y+cross(2z)=-14+18}}}

{{{2y=4}}}

{{{y=4/2}}}

{{{y=2}}}..........plug in 3

{{{-x+6y-32=35}}}.............3

{{{-x+6*2-32=35}}}

{{{-x+12-32=35}}}

{{{-x=35+32-12}}}

{{{-x=55}}}....multiply by {{{-1}}}

{{{-x(-1)=55(-1)}}}

{{{x=-55}}}............plug {{{x}}} and {{{y}}} in 1 and find {{{z}}}



{{{x+y+z=-9}}} ..............1


{{{-55+2+z=-9}}} 

{{{z=-9+55-2}}} 

{{{z=44}}} 


so, your solutions are:

{{{x=-55}}}

{{{y=2}}}

{{{z=44}}}


check:

{{{2x+4y+2z=-14}}}...........2 

{{{2(-55)+4*2+2*44=-14}}}

{{{-110+8+88=-14}}}

{{{-110+96=-14}}}

{{{-14=-14}}}