How does God forgive sins without clearing the guilty?

The tension between God's justice and His mercy is beautifully resolved in the doctrine of atonement. As presented in Exodus 34:7, God cannot clear the guilty because that would contradict His nature as a righteous judge. However, in His infinite wisdom, God provided a solution through Christ, where justice and mercy met at the cross. Christ bore the punishment for the sins of those He came to save, being made sin for us in 2 Corinthians 5:21. This ensures that God's justice is upheld, as sin is fully punished in Christ, while simultaneously allowing for the forgiveness of the believer's sins. Thus, God can justly declare sinners righteous because their sins have been imputed to Christ, and His righteousness is imputed to them, fulfilling the demands of justice.