It is impossible to keep the 10 Commandments. Why? Because they reflect the nature and character of God. God is telling Israel what He is like and by extension what they are not like. They discover that they cannot follow those ten “simple” rules. The Old Testament is full of examples of their failure, but we can look at our own lives for plenty of examples without having to resort to digging through Genesis through Malachi.
If you question this take a look at Galatians 3:21 – 25. There Paul tells us that the Law essentially leads us to faith in Christ. He expands this in Romans 3, verse 20 is especially telling. He states there that the Law essentially reveals our state. It tells us that we are in a state of sin, it is our nature. We are different from God, therefore sin.
So sin is not something we do. Sin is our nature. The Law points that out and communicates that the only way to resolve that is for Christ to pay the price for our state. That is the message of Romans 6. That is the Gospel.
Our only response to sin is to accept Christ’s death for it.