Newton's Method of Solving Non-linear Systems Questions

[EWW]

Question on Newton’s Method of solving systems of non-linear equations. I understand the concept for a single non-linear y=f(x) solved for zero, but am confused about systems of non-linears. If I take two functions U(x,y) and V(x,y), am I solving for the points where they intersect with each other AND the xy plane ? Also, in a paper I’ve been studying (Geometrical Aspects of Newton’s Method by Walter Jennings, Mathematics Magazine, Vol. 42, No. 5, Nov., 1969, pp.262-266) there is the following statement- All solutions of the system U(x,y) and V(x,y) are zeros of the function T(x,y) = (U^2(x,y) + V^2(x,y)) ^ 1/2. Where did this equation come from ? Thanks . . . EWW

 

[mathman]

All solutions of the system U(x,y) and V(x,y) are zeros of the function T(x,y) = (U^2(x,y) + V^2(x,y)) ^ 1/2. Where did this equation come from ? Thanks . . . EWW

As long as U and V are real, T=0 if and only if both U and V are 0, since U^2 and V^2 can never be negative.