Instead of trying to solve for each individual variable, try solving for (x+y), (xy), and (a+b). I picked two of the given equations: ax^2 + by^2 = 10 and ax^3 + by^3 = 50. Then I multiplied each equation by (x+y). I hoped by doing this, I would be able to simplify and compare the resulting equations. See if you can pick up from where I left off and solve the problem. If you need another hint, press the Hint #2 button below.