solve for x,y,z

Answer 1

-12x -12z = -6 divide by -6 to get 2x +2z = 1,

divide by 2 and get x+z = 1/2

12x -9y =0, divide by 3 to get 4x-3y = 0

-9y +12z = 0, divide by 3 to get -3y +4z =0

that reduces the system to

x+z = 1/2

4x-3y = 0

-3y +4z = 0

subtract the last two to get 4x-4z = 0, divide by 4 to get x-z = 0,

combine that with x+z = 1/2

x-z=0

x+z = 1/2

add them to eliminate z and get

2x = 1/2

x = (1/2)/2 = 1/4

x = 1/4

z = 1/4

y = 1/3

4x=3y

4(1/4) = 3y

3y=1

y = 1/3

solution is (x,y,z) = (1/4,1/4,1/3)

check the solution, plug the values into the

original 3 equations and see if they work

12x-9y=0

12(1/4) -9(1/3) = 0

3 -3 = 0

0 = 0

-9y+12z =0

-9(1/3) +12(1/4) =0

-3 +3 =0

0=0

-12x-12z = -6

-12(1/4) - 12(1/4) =-6

-3 -3 = -6

-6=-6

it works, for all 3 equations