How To Get Latias/Latios in Pokémon Ruby/Sapphire/Emerald Version
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Note: You must become Pokémon League Champion before finding Latias or Latios.
For Pokémon Ruby and Sapphire: After beating the Champion, you can watch Television and it will inform you a Red or Blue flying Pokémon is wandering around Hoenn.
If you have Pokémon Ruby Version, you will find Latios.
If you have Pokémon Sapphire Version, you will find Latias.
If you have Pokémon Emerald Version, you will have the chance of choosing one or the other. (Latios or Latias).
This time it took a little longer, you never know whether or not it'll be a quick find or a long search. My point is, be patient! The duo travels each and every route once you enter and exit an area. Be sure to have a Pokémon under Level 40 so the Repel won't work for it to appear.
Good luck!