
Lagrangian function.
f(x,y)=2x^2+y^2 subject to the constraint of x+y=1.
I understand how to set it up and how to find f with respect to x y and L.
fx=4x+L
fy=2y+L
fL=x+y1
So, again...I understand the cal part of it, but fail to remember the basic allgebra part. Please solve for x, y, and L (ie the critical point)

set $\displaystyle f_x, f_y$ and $\displaystyle f_L = 0$ then solve the system.

I know to set them equal to 0, but I'm not exactly sure how to solve from there. This may actually be the wrong section since this is just algebra...

$\displaystyle f_x=4x+L=0$ ...(1)
$\displaystyle f_y=2y+L=0$ ...(2)
$\displaystyle f_L=x+y1=0$ ...(3)
Using (1) and (2)
$\displaystyle 4x+L=2y+L$
Therefore
$\displaystyle 4x=2y$
$\displaystyle 2x=y$
Putting this into (3)
$\displaystyle x+2x1=0$
$\displaystyle 3x1=0$
$\displaystyle x=\frac{1}{3}$
Can you solve it from here?

Oh, I feel dumb now... Thank you!