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

• To: mathgroup at smc.vnet.net
• Subject: [mg101213] Re: [mg101149] How to feed a list of xy pairs into Solve to output
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Fri, 26 Jun 2009 06:55:48 -0400 (EDT)
• Reply-to: hanlonr at cox.net

```list = {{1, 2}, {3, 1}, {5, 4}, {6, 3}, {2, 5}};

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

{{1, 2, -13}, {3, 1, -21}, {5, 4, -45}, {6, 3, -47}, {2, 5, -31}}

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

{{1, 2, -13}, {3, 1, -21}, {5, 4, -45}, {6, 3, -47}, {2, 5, -31}}

{x, y, z} /. {Reduce[{6 x + 4 y + z == 1, 0 < x < 7, 0 < y < 6}, z,
Integers] // ToRules}

{{1, 1, -9}, {1, 2, -13}, {1, 3, -17}, {1, 4, -21}, {1, 5, -25},
{2, 1, -15}, {2, 2, -19}, {2, 3, -23}, {2, 4, -27}, {2, 5, -31},
{3, 1, -21}, {3, 2, -25}, {3, 3, -29}, {3, 4, -33}, {3, 5, -37},
{4, 1, -27}, {4, 2, -31}, {4, 3, -35}, {4, 4, -39}, {4, 5, -43},
{5, 1, -33}, {5, 2, -37}, {5, 3, -41}, {5, 4, -45}, {5, 5, -49},
{6, 1, -39}, {6, 2, -43}, {6, 3, -47}, {6, 4, -51}, {6, 5, -55}}

Bob Hanlon

---- Bill <WDWNORWALK 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.

```

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