Find the extrema of the function $f(x,y,z)=x+y+z$ subject to the constraints $x^2-y^2=1$ and $2x+z=1$
So I have $G(x,y,z,\lambda_1,\lambda_2)=x+y+z-\lambda_1(x^2-y^2-1)-\lambda_2(2x+z-1)$
$1-2\lambda_1x-2\lambda_2=0$
$1+2\lambda_1y=0$
$1-\lambda_2=0$
plus the initial constraints, rearranging and substituting gives
$\frac{1}{4\lambda_1^2}-\frac{1}{4\lambda_1^2}=1$
-->$0=1$?
Have I done something wrong here or is it just not possible to find an extrema?