From the first equation x - 2y = 2, we isolate y to get y = (x - 2) / 2. Substituting this into the second equation xy = 2 results in x multiplied by ((x - 2) / 2), which equals 2. Multiplying the entire equation by 2 and expanding gives x2 - 2x = 4. Rearranging all terms to one side yields the quadratic equation x2 - 2x - 4 = 0.