There are several answers, depending on the interpretation of the question. Here are some of them.
(1) 2/(3x+y)=5/(x-2y)=17/3?
Take one pair of the expressions:
2/(3x+y)=17/3, cross-multiplying:
6=17(3x+y)=51x+17y, 17y=6-51x, so 34y=12-102x.
Take another pair of the expressions:
5/(x-2y)=17/3, cross-multiply:
15=17(x-2y)=17x-34y, substituting for 34y:
15=17x-12+102x,
27=119x, x=27/119; 17y=6-51x=6-51(27/119)=6-81/7=(42-81)/7=-39/7, y=-39/119.
So x=27/119, y=-39/119.
(2) [2/(3x)]+y=(5/x)-2y=17/3?
[2/(3x)]+y=17/3, multiply through by 3x:
2+3xy=17x,
3xy=17x-2, so 6xy=34x-4.
(5/x)-2y=17/3, multiply through by 3x:
15-6xy=17x, substitute for 6xy:
15-34x+4=17x,
19=51x, x=19/51,
2+(19/17)y=17(19/51)=19/3,
(19/17)y=19/3-2=13/3,
y=(13/3)(17/19)=221/57.
So, x=19/51, y=221/57.
(3) ⅔x+y=5/(x-2y)=17/3?
2x+3y=17, x=½(17-3y).
15=17x-34y=17(17-3y)/2-34y,
30=289-51y-68y=289-119y,
119y=259, y=259/119=37/17.
x=½(17-111/17)=178/34=89/17.
So, x=89/17, y=37/17.