If Jesus could not sin, His temptation was a sham.
Well he chose to not sin, and because of that He could not sin.
Because He decided He would be faithful to the Father and not sin, it's a moot point on whether He could have sinned or not because He made the decision to not sin and because of that - He never sinned.
1 John 3:9 tells us that "Whosoever is born of God doth not commit sin; for his seed remaineth in him: and he cannot sin, because he is born of God."
This is what Jesus did and it's why He could not sin. It's what 1 John 3:9 is talking about and it's what Christians should be doing rather than going around claiming "I'm a sinner" like the tares