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Math: Systems Of Equations help

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80 for fulfilling my request - Virtual OK - Posted Apr 13, 2019

Summary: How can I find the closest possible positive values to solve a system of equations for many variables and equations?

First let me give a concrete example of my problem:

A concrete example:

If I have a given set of ingredients, let's say apples, chicken, and butter

Per 100g
Apple:______fat: 0g_____protein: 1g _____carbs: 16g
Chicken:___ fat: 4g_____protein: 20g____carbs: 0g
Butter: ____ fat: 100g __protein: 0_______carbs: 0g

And I want to eat a given amount of nutrients, let's say 20g of fat, 22g of protein, and 10g of carbs .

Fat 20 ≈ 0a + 4c + 100b
Protein 22 ≈ 1a + 20c + 0b
Carbs 10 ≈ 16a + 0c + 0b

a= Amount of apple (1=100grams of apple)
c= Amount of chicken
b= Amount of butter

How much of each food should I eat to get as close as possible to my desired nutrients?

I need to be able to solve problems like these where the amount of ingredients (variables) can vary, and the amount of nutrients(equations) can vary. Though for now, it is less important that the amount of equations vary as long as I can solve for three equations (fat, carbs, protein).

So here are my abstract questions:

1. How do I solve systems of equations where there can be many equations and many variables.
Ex: We should be able to solve for any of these:

1.
10≈1x+7y +6z
6 ≈ 2x+1y +12z
15≈5x+2y +3z

2.
40≈1x+7y +6z +8g + 10a +7f
60 ≈ 2x+1y +12z +9g + 3a + 8f
14≈5x+2y +3z +4g +7a +3f

3.
10≈1x+7y +6z
6 ≈ 2x+1y +12z
15≈5x+2y +3z
20≈1x+7y +6z
68 ≈ 2x+1y +12z

2. The variables can't equal negative values since you can't have a negative amount of food. If the only solution uses a negative value, how can I find an option with the closest possible positive amount?

This is what I mean by closest possible:

For example's sake, pretend that the only true solution to this system of equations gives us at least one negative variable:

10≈1x+7y
6 ≈ 2x+1y
15≈5x+2y

If x=3 and y =1 , then the difference between our left side and and right side is an absolute value of 3.

10≈10_________+0
6 ≈ 7 __________+1
15≈17 _________+2
——————————
Total difference: 3

But are there values for x and y that would give a smaller total difference? How do we find that value?

Reviews of Dashiell


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Inactive User received unit of 30 Min Play Session from Dashiell
Jul 07, 2019
I pray all goes well with you
Dec 15, 2018
Detailed and methodical. She already is very conscious in her eating, so the task seemed to a short step for her.
Caitlin received hour of Talk About Lucid Dreaming from Dashiell
Dec 06, 2018
Dash is wonderful! I learned so much about Lucid dreaming and hope to have so more in the future. I look forward to our future coaching and lucid sess...ions. Thanks for bringing so much awareness and insight! show more
Nov 21, 2018
Really helpful. Gave me great tips!
Damla received unit of 30 Min Play Session from Dashiell
May 12, 2018
Yayy. Love her. Beautiful, super fun game. Can’t wait to play again. A super smart, and funny person.
Daniel received hour of Lucid Dreaming Training from Dashiell
Mar 26, 2018
Dashiell is responsive and helpful!
Aurore received hour of Instagram Help from Dashiell
Feb 12, 2018
Dashiell was amazing, very knowledgeable and friendly. I will happily work with her again :)
Jenn received hour of Lucid Dreaming Training from Dashiell
Jan 20, 2018
This was a great session with Dashiell - she knows her stuff and was easy to talk to. She provided a great overview of lucid dreaming, along with prac...tical tips and tools to help me get started. Much appreciated!show more
Monique provided session of Discuss Steemit with you for 30 min for Dashiell
Jan 07, 2018
Dashiell asked great questions and was easy to work with. I think she'll do really well :)
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Jan 05, 2018
Very fun and informative, so helpful. And really did her research. Shows that she is dedicated. Worth every Simbi and more!


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About Dashiell Bark-Huss

When I was 19 I trained myself to lucid dream frequently so that I could eat all the junk food I love in my dreams, while eating a strict raw paleo diet in the physical world. To this day I still use... lucid dreaming to eat junk food but I've explored many other applications for lucid dreaming. I want to share lucid dreaming with more people. I founded and ran Dream Hackers Club at Chicago's hackerspace Pumping Station One, a club that explored how technology could be used in conjunction with dreaming. Later, I co-ran the Chicago Lucid Dreamers Meetup group for some time where I conducted a weekly lucid dreaming book club and workshop. show more

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