1. (16) Consider the system of equations 21 + 2 + 3 3 = 4 1 2 12 33 = 6 a.) (8) Does the system implicitly define 1 and 2 as functions of 3 in the neighbourhood of the point (1 = 1 2 , 2 = 2, 3 = 3) ? Justify your answer with reference to the implicit function theorem. b.) (8) If yes, find an expression for 23 . What is the value of this derivative at the given point?

Question: 1. (16) Consider the system of equations 2x1+ X2 + 2 *3 = 4 #X1x2X3 = 6 a.) (8) Does the system implicitly define x1 and x2 as functions of X3 in the neighbourhood of the point (x1 = ), X2 = 2, X3 = 3) ? Justify your answer with reference to the implicit function theorem. b.) (8) If yes, find an expression for dx2/dx3 . What is the value of this derivative at the given point