We have to understand that it is NOT our faith that saves us, it is the OBJECT of our faith. What does Jesus mean when he says “According to your faith be it done to you?” It means that they actually believed in Him as the Messiah. It was the OBJECT of their faith, Jesus, that was the factor behind the healing of their blindness. They are crying out for Him to heal them and they call Him, “son of David,” that is a messianic term; they believed Jesus was the Messiah.
At the end of the Sermon on the Mount Matthew talks about people being astonished because Jesus spoke as one who had authority (Matthew 7:28-29 And when Jesus finished these sayings the crowds were astonished at his teaching for he was teaching them as one who had authority). In the follow 2 chapters (Matthew 8-9) he goes on to give us 14 ways Jesus proved that authority by His actions. In Matthew 8-9, Matthew is trying to get us to see that authority because it is not only the authority of a King, but also the authority of our great God.