Can anyone help with this problem please? I understand the concept of the langrange multiplier but this ones stumping me.

F(x,y)=2x+y subject to the ellipse g(x,y)=X^2+25y^2=1

I have f(x,y)=2i-1j. g(x,y)=2xi+50yj

When I apply the lamb though I get 2=lambda 2x. Which means lambda=1/x which doesn't make sense.

Can anyone tell me where I am wrong with is one?