In this attached circuit, when $R_1=0\Omega$, I am failing to understand how the two cells affect the potential difference across the central resistor R3. I understand that potential difference is constant across different strands in parallel, and that so 12 volts should be distributed between R2 and R3 as a potential divider, and so 9V should be across R3 from V2. Likewise, from V1, 10V will cross R3 from V1, and so the total potential difference across R3 should be 19V.
However, according to the answer sheet, the potential difference across R3 is 10V. Is my misunderstanding here conceptual, or something more basic, and why does potential difference act in this way?