Lagrange Multipliers - basic which value?

[rocomath]

(1) f(x,y,z)=x+2y
(2) x+y+z=1
(3) y^2+z^2=4

1=\lambda
2=\lambda+2y\mu
0=\lambda+2z\mu

u=\frac{1}{2y}
y=\pm\sqrt2 \ \ \ z=\pm\sqrt2

Plugging into equation 2 to solve for x.

How do I know to use either y=\sqrt 2 \ \mbox{or} \ y=-\sqrt2 ... similarly with my values for z.

edit: NVM, I'm an idiot :p I overlooked a step, which told me that z=-y

... too late to delete?

 

[rootX]

see the geometry (It's a plane)

f(x,y) = ..

I was thinking about f_xx*f_yy - (f_xy)^2 thing,
but my teacher says it's very hard to *identify* max min in Lagrange; should use geometry