Question

Show that the two equations
2e^u + vx − y^2 = 3
u + vz^2 + x^2− z sin u = 5
are satisfied at the point (u, v, x, y, z) = (0, 1, 2, 1, 1). Why do these equations determine u and v as functions of (x, y, z) when (u, v, x, y, z) is close to (0, 1, 2, 1, 1) ? Find ∂u/∂z and ∂v/∂z when (u, v, x, y, z) = (0, 1, 2, 1, 1).