I just removed a wall that was separating my livingroom and my kitchen and now they are two different levels. My kitchen is about a inch lower than the living room.my kitchen is drywall and my living room is ceiling tile how could I join the two rooms without building a header to go over it

You could bring the livingroom ceiling down to the kitchen level or you can install a piece of 5/4" wood over the area where you removed the wall plate.

5/4 will measure about an inch thick. You can cut a 45 degree bevel on the edge towards the livingroom side so you won't have a square edge.