What a strange question. It seems like a contrived mathematical question more than a circuits question because I don't think those are normal voltage sources...in a normal voltage source, there is a parasitic resistance, so dV/dI would be a constant equal to the resistance. Put another way, the graph of voltage vs. current would be a straight line that intersects at the origin with 0V and 0 Amps.
Anyway, using circuit theory, I'd say you can use a couple of pieces of information to solve it. First, it's a single loop, so the currents in the two sources must be equal. Second, the sum of the two voltages equals the voltage across the 1 ohm resistor (by KVL), which is numerically equal to the current since it's 1 ohm.
I think between those two items, and writing the current/voltage equations of the two voltage sources (like Vx = 4 - 2 * Ix), and a bunch of algebra, you'll get there. Good luck.
