This is just like solving equations by succesive elimination. For example, I see that adding (1) and (2), I eliminate y1: (1)+ (2) gives -2y2+ 4y3.

Also adding (1) and (3) elimininates y1: (1)+ (3) gives y2- 2y3. Now I see that if I add the first of those to 2 times the second everything cancels! That is ((1)+ (2))+ 2((1)+ (3))= 3(1)+ (2)+ 2(3)= 0.

(No, I am not claiming 3+ 2+ 6= 5 . (1), (2), and (3) refer, of course, to the three inequalities.)

What do you get doing the same to the right side?