A carbon capture system is used to remove carbon dioxide from flue gas emissions. The system consists of a first scrubbing column, a carbonating tower, and a separation system. In the first scrubbing column, nitrates and sulfates are removed from the flue gas, producing a purified flue gas and a bottoms product containing the sulfates and nitrates. The purified flue gas is then transferred to a carbonating tower, where it is contacted with a solution (such as brine, ammonia, or a weak base) to remove carbon dioxide, producing a lean brine solution. The lean brine solution is then filtered to recover sodium bicarbonate or soda ash.