6. (20 points) Consider the system of equations
3x2y − xz + wz = 3
xy − yz + 2wx = −4atthepointx=1,y=2,z=1,w=−2. Canweviewyandwasfunctionsofxand
z? If so, find ∂w.∂z
I am having trouble understanding why dw/dz is -1 rather than one, as the Implicit function theorem has a negative sign when it is used. Any quick help would be greatly appreciated. Thanks!