x=206-z, so x+y=206-z+y=166, and y=z-40, therefore y+z=z-40+z=335, 2z=375, z=375/2.
x=206-z=206-375/2=37/2; y=z-40=375/2-40=295/2.
CHECK
x+z=37/2+375/2=206✔️; x+y=37/2+295/2=166✔️; y+z=295/2+375/2=335✔️
x+y+z=37/2+295/2+375/2=707/2, not 427.
x+z+x+y+y+z=2(x+y+z)=206+166+335=707, so x+y+z=707/2.