I have a Utility Function U(x,y) and I am trying to maximize x, y, subject to p1x+p2y=M where M is my available money. I know I need to set up a lagrange:

L: U(x,y) + g(p1x+p2y-M)

But I feel like I'm missing something because when I take the first order conditions I'm only getting the constraint values. ex: dL/dx: dU/dx +gp1
It seems like I should have another x value coming out of this but I can't remember how that happens.

Any help greatly appreciated!