Here are the steps to solve this problem:
1. Apply KVL around the loop containing V1, R1, and R2:
V1 - I1R1 - I1R2 = 0
2. Apply Ohm's law at R1 and R2 to substitute for I1:
V1 - (V1/R1)R1 - (V1/R1)R2 = 0
3. Simplify the equation:
V1 - V1 - V1(R2/R1) = 0
4. Solve for V1:
V1(1 + R2/R1) = 0
V1 = 0