2x +3y=0 and 3x-y=0
If you add y to both sides of the second equation it becomes
3x = y
Hence, in the fi8rst equation you can replace y by 3x to get
2x + 3(3x) = 0
2x + 9x = 0
11x = 0
and hence x = 0. If you now substitute x = 0 into either equation you started with you will find that y = 0.
Thus the solution is x = y = 0.