In a water softener, the brine serves to flush the accumulated minerals from the resin collectors.
Carbon is used to filter impurities (chemicals) out of the water.
One is not a substitute for the other. They serve different purposes. Have your water analyzed to see what you need. ie) If you have hard water, get a softener. If you have a lot of chemicals in the water such as chlorine, etc get a filter. Too much iron requires a third type of water purifier.