2Z+5X=13Y+1000.(1)
13Z+3Y=9X.(2)
6X+8Y+600=5Z.(3)
(1)*9+(2)*5:
83z+15y=117y+9000,83z-102y-9000=0.(4)
(2)*2+(3)*3:
26z+30y+1800=15z,11z+30y+1800=0.(5)
z=7200/301
y=-20700/301
x=3500/301