Suggestions with ましょう and ましょうか

Replace ます with ましょう to make a polite suggestion: 行いきます → 行いきましょう (“Let’s go”), and 食たべます → 食たべましょう (“Let’s eat”).

Add か to ask for a decision: 行いきましょう か can mean “Shall we go?” Depending on the situation, ましょうか can also offer to do something for the listener. Context tells you whether English needs “we” or “I.”

一緒いっしょ に means “together.” 一緒いっしょ に 昼ひる ご飯はん を 食たべましょう invites someone to have lunch with you: “Let’s have lunch together.”