Bearing in mind this was posted in the homework section, I think the OP's course had introduced mesh analysis and was leading up to formal matrix methods. My post #7 furthers this aim.
I further think that the OP got these ideas confused with Kirchoffs laws, as often happens if Kirchoff is introduced at an earlier stage.
I further think that the OP got these ideas confused with Kirchoffs laws, as often happens if Kirchoff is introduced at an earlier stage.