Try comparing some scripture with scripture.
Which is how one is suppose to interpet scripture, not run to Lexicons and Interliners. (1Cor.2:13)
It was the Jews who killed the Lord and Peter says it was the House of Israel (Acts.2:36), thus, those people who were from the Northern Kingdoms were called Jews.
And that was the title that was put over the Lord's head, King of the Jews, and that was who He asked His Father to forgive, those who crucified Him, the Jews, from both Houses.
[Acts 2:36] Therefore let all the house of Israel know assuredly, that God hath made the same Jesus, whom ye have crucified, both Lord and Christ. The next line in scripture says: verse 37 "Now when they heard this, they were pricked in their heart, and said unto Peter and to the rest of the apostles, Men and brethren, what shall we do?" So....these are the folks that Peter is referring to when he says "Whom ye have crucified".
Who are these folks? It's not ALL The House of Israel who crucified him. Peter is telling everyone to let ALL the Israelites know about this situation....and indeed that was their commission from The Lord: [Matthew 10:5-6] Go to the House of the Lost Sheep of Israel.
Peter is talking to: verse 5....And there were dwelling at Jerusalem Jews, devout men, out of every nation under heaven. These were the folks being addressed by Peter....they were gathered in Jerusalem for Shavuot. They were not the same folks Peter was referring to when he said ALL the House of Israel.....because they, the Jews, constituted only 1/12 of the House of Israel.
I win!