Question

I need help solving this three variable equation
10x+6y+8z=100
10x+12y+6z=100
5x+4y+12z=100

Answer 1

from eqn 1 and eqn 2,
10x+6y+8z=100=10x+12y+6z
10x+6y+8z=10x+12y+6z
6y+8z=12y+6z
3y+4z=6y+3z
z=3y---------------eqn 4
from eqn 1 and eqn3
10x+6y+8z=100 =5x+4y+12z
10x+6y+8z=5x+4y+12z
5x+2y=4z
now from eqn4
5x+2y=4(3y)
5x=10y
x=2y--------------eqn 5
substituting value from eqn 4 and eqn 5 to eqn 1
10(2y)+6y+8(3y)=100
20y+6y+24y=100
50y=100
y=2 then x = 4 and z = 6