1. The problem statement, all variables and given/known data Find the equations for the utility maximizing values for x and y U(x,y) = x^2 + y^2 2. Relevant equations Budget constraint: I = PxX +Pyy L(x,y,\lambda ) x^2 + y^2 + \lambda (I - PxX - PyY) 3. The attempt at a solution I got the three partial derivatives and set equal to zero: dL/dx = 2x - \lambda Px = 0 dL/dy = 2y - \lambda Py = 0 dL/d\lambda = I-PxX-PyY = 0 Then i set the first two equal to each other to try and find x in terms of y 2x = \lambda Px 2y \lambda Py This results in x = PxY/Py But here's the problem... When I plug that into the last equation, i get stuck I get: I - PxX - Py(PyX/Px) = 0 I dont know how to proceed from here algebraically. Normally I'd be able to cancel on some of the simpler problems. But I can't cancel the Px out from the denominator Any help would be greatly appreciated!!!