from the 1st : y = 10/13
from the 3rd: x = 13z/16
sub into 2nd
x+y+z = 39
(13z/16) + 10/13 + z = 9
times 208
169z + 160 + 208z = 1872
377z = 1712
z = 1712/377
now back-substitute ....
13y=10
x+y+z=39
16x=13z
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