How does Christ's righteousness impact salvation?

In sovereign grace theology, the righteousness of Christ is crucial for salvation because it is through His obedience that believers are made righteous. When a person repents and believes in Christ, they are not only forgiven but also receive the righteousness of Christ as a gift. This is rooted in the understanding that Christ fulfilled the law perfectly on our behalf and bore our sins on the cross. As stated in Psalm 51:14, David acknowledges the necessity of God's righteousness, underscoring that for the repentant sinner, it is through Christ alone that we can stand justified before God. Therefore, our salvation is anchored not in our own righteousness but wholly in Christ's righteousness, which is granted to all who believe.