How to feed a list of xy pairs into Solve to output xyz triplets

*To*: mathgroup at smc.vnet.net*Subject*: [mg101149] How to feed a list of xy pairs into Solve to output xyz triplets*From*: Bill <WDWNORWALK at aol.com>*Date*: Thu, 25 Jun 2009 07:13:38 -0400 (EDT)

Hi: Let's say that I have a list of xy coordinate pairs: list= {{1,2}},{3,1},{5,4},{6,3},{2,5}}. Now I'd like to find xyz triplets using Solve for the equation 6*x + 4*y + z == 1. xyz results: {{1,2,-13}},{3,1,-21},{5,4,-45},{6,3,-47},{2,5,-31}}. (I used Solve 5 times.) Question: How do I code that into Mathematica for a "one shot output?" (Use Solve once.) Thanks, Bill Mathematica 6.0.1 using Win XP on a pc.

**Follow-Ups**:**Re: How to feed a list of xy pairs into Solve to output xyz triplets***From:*Sseziwa Mukasa <mukasa@jeol.com>