x-2y-3z=0 ①
2x+y-2z=0 ==> 4x+2y-4z=0 ②
①+2*②==>5x-7z=0 ==>x:z=7:5
x-2y-3z=0 ==> 2x-4y-6z=0 ③
2x+y-2z=0 ④
④-2*③==>5y+4z=0 ==>y:z=-4:5
x:z=7:5
y:z=-4:5
==>x:y:z=7:(-4):5
x-2y-3z=0 ①
2x+y-2z=0 ==> 4x+2y-4z=0 ②
①+2*②==>5x-7z=0 ==>x:z=7:5
x-2y-3z=0 ==> 2x-4y-6z=0 ③
2x+y-2z=0 ④
④-2*③==>5y+4z=0 ==>y:z=-4:5
x:z=7:5
y:z=-4:5
==>x:y:z=7:(-4):5