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