KCL in 3 loops circuit and two batteries?
V1 and R1 are parallel, so the voltage across R1 is determined completely and always by V1. Therefore, the current is determined by V1/R1. Always.
V2 and R2 are parallel, so the current through R2 is likewise determined by V2 only.
V1 and V2 are not parallel. Resistor R3 connects between them. The current through R3 will depend on the difference between V1 and V2.