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

• To: mathgroup at smc.vnet.net
• Subject: [mg101179] Re: How to feed a list of xy pairs into Solve to output xyz triplets
• From: computer algebra <mike.honeychurch at gmail.com>
• Date: Fri, 26 Jun 2009 06:48:57 -0400 (EDT)

On Jun 25, 6:12 am, Bill <WDWNORW... at aol.com> wrote:
> 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.

Solve[6*x + 4*y + z == 1, z] /. {x -> list[[All, 1]], y -> list[[All,
2]]}

gets you a one shot list of z. Mapping list onto the structure you
want gets you a one shot x,y,z

{#[[1]], #[[2]], Solve[6*#[[1]] + 4*#[[2]] + z == 1, z][[1, 1, 2]]} & /
@ list

Mike

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