\(\displaystyle f(x,y,z,) = (4x - 1/2y + 27/2 z)\)

on the surface of \(\displaystyle g=x^4+y^4+z^4=1\)

I have already put \(\displaystyle \bigtriangledown f = \lambda \bigtriangledown g \)

Getting the following 4 equations... Where do I go from here?

\(\displaystyle 4\lambda x^3=4\)

\(\displaystyle 4\lambda y^3=-1/2\)

\(\displaystyle 4\lambda z^3=27/2\)

\(\displaystyle x^4+y^4+z^4=1\)