After deriving |A|, the its value can be projected onto the curve of Token B, which is currently in Surplus at point B1. As token swaps must result in an equivalent exchange of value, the shaded area between points B1 and B2 ("|B|") will be exactly the same as |A|. With that, we can solve for B2 to calculate the new Current Balance after the trade is executed, and after dividing the quantity of Token B received by the quantity of Token A sold, we can determine the exchange rate for any two tokens liquidity pool in a manner that does not rely on pairing.