Question 1081861
x+y= 12  ==>  x = 12-y
y+z=10  ==>   z = 10-y
z+x=8   ==>  (12-y) + (10-y) = 8  

 22 - 2y = 8 —>  y=7 —> x=5, z=3
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Ans:  x=5, y=7, z=3

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Check:  x+y = 7+5 = 12 (ok)
              y+z = 7+3 = 10 (ok)
              z+x = 3+5 = 8 (ok)