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Solving Systems of Equations... Elimination Method (NancyPi) Teacherflix 15 Views • 2 years ago

MIT grad shows how to use the elimination method to solve a system of linear equations (aka. simultaneous equations). To skip ahead: 1) For a BASIC example where terms cancel right away when you add the equations, skip to 0:25. 2) For an example in which you have to MULTIPLY ONE EQUATION by a number before adding the equations, skip to time 6:26. 3) For an example in which you have to MULTIPLY BOTH EQUATIONS by numbers before adding, skip to 12:12. P.S.) For HOW TO SUBTRACT equations instead of adding them, if you'd rather do that, skip to 18:00. Nancy formerly of MathBFF explains the steps.

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For how to solve a system of linear equations by the SUBSTITUTION METHOD, jump to: https://youtu.be/YriMMWbndn0

What does it mean to solve a system of equations using the elimination method? It means to solve for the x and y values that make both equations true, using the elimination method. Elimination is just one way of solving (substitution is another way) and is sometimes called linear combination. Here's how:

1) BASIC ELIMINATION: First, make sure the equations are ordered in the same way, with their like terms lined up vertically. Then, try adding the equations (vertically) to make a new equation. If a term in the first equation has the same number coefficient but opposite sign (like 5y and -5y), then adding the equations will mean that those terms cancel. Since those terms disappear (in the example, 5y and -5y), there is just the variable x left in the equation so you can solve for x. Once you solve for x, you can take that number and plug it in for x in either of the original equations in the system, to solve for the other variable, y. The (x,y) pair is your solution.

2) MULTIPLY ONE EQUATION BEFORE ADDING: Sometimes terms don't immediately cancel when you add the two equations. What do you do then? Try multiplying one of the equations by a number (both the left and right sides) to make either the x terms or y terms have similar coefficients (but opposite sign), like positive 4x and negative 4x. Then add the two equations (the new version) and follow the same steps as in the first example.

3) MULTIPLY BOTH EQUATIONS BEFORE ADDING: If it does not help to just multiply one equation by a number, you may need to multiply both equations, separately, by numbers. If you check to see whether you can just multiply one equation by a number and add opposite terms/eliminate a variable, and it is not possible, then aim for an LCM, or least common multiple, by multiplying each equation by a different number, and then adding the equations.

P.S.) YES, YOU CAN SUBTRACT INSTEAD (if you want): If you have a system that has the exact same x terms or exact same y terms in both equations, if you prefer, you can just subtract the equations. Alternatively, if you still wanted to add the equations, you could just multiply one of the equations by -1 first and then add the equations and solve normally.

IMPORTANT: If you get something like 0 = 0 or 8 = 8, or something like 1 = 2 or 0 = 21 when you are following these steps and trying to solve, then you have probably found a special case. If you get something TRUE like 0 = 0 (a number equals the same number), then there are an infinite number of solutions to the system, and you can just write "infinitely-many solutions". If instead you get something FALSE like 0 = 21, then there is no solution (inconsistent system), and you can write "no solution".

For more of my math videos, check out: http://nancypi.com

How To Simplify Complex Fractions Teacherflix 9 Views • 2 years ago

Every Animal In Your DNA Teacherflix 9 Views • 7 months ago

You are the living ancestor of an unbroken chain of lives stretching from you, through your mother and your grandmother all the way back through the complete history of life on planet Earth to the very first life forms that appeared around four billion years ago.

#naturalhistory #DomainOfScience

You can buy this poster here: https://www.redbubble.com/people/dominicwalliman/works/28504585-the-chain-of-life-your-evolutionary-history?asc=u&p=poster&rel=carousel
Get all my other posters here: https://www.redbubble.com/people/dominicwalliman

And free downloadable versions of this and the other posters here. If you want to print them out for educational purposes please do! https://www.flickr.com/photos/95869671@N08/

More info and links:
Times humans nearly became extinct
https://io9.gizmodo.com/close-....calls-three-times-wh
Bottlenecks of human population
https://academic.oup.com/mbe/a....rticle/17/1/2/975516
Animal Ancestors illustration
https://ntamura.deviantart.com..../art/Evolution-proje
Timeline of the evolutionary history of life on Earthh
https://en.wikipedia.org/wiki/....Timeline_of_the_evol
Early sponge
http://www.sciencemag.org/news..../2015/03/oldest-know
List of phylogeny of human ancestors
https://biology.stackexchange.....com/questions/27992/
Acorn worm genes shared with humans
http://www.scienceworldreport.....com/articles/33346/2

Thanks so much to my supporters on Patreon. If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much. https://www.patreon.com/domainofscience
The Great Courses Plus is currently available to watch through a web browser to almost anyone in the world and optimized for the US market. The Great Courses Plus is currently working to both optimize the product globally and accept credit card payments globally.
I also write a series of children’s science books call Professor Astro Cat, these links are to the publisher, but they are available in all good bookshops around the world in 18 languages and counting:
Frontiers of Space (age 7+): http://nobrow.net/shop/profess....or-astro-cats-fronti
Atomic Adventure (age 7+): http://nobrow.net/shop/profess....or-astro-cats-atomic
Intergalactic Activity Book (age 7+): http://nobrow.net/shop/profess....or-astro-cats-interg
Solar System Book (age 3+, available in UK now, and rest of world in spring 2018): http://nobrow.net/shop/profess....or-astro-cats-solar-
Solar System App: http://www.minilabstudios.com/....apps/professor-astro
And the new Professor Astro Cat App: https://itunes.apple.com/us/ap....p/galactic-genius-wi

Find me on twitter, Instagram, and my website:
http://dominicwalliman.com
https://twitter.com/DominicWalliman
https://www.instagram.com/dominicwalliman
https://www.facebook.com/dominicwalliman

The Map of Chemistry Teacherflix 6 Views • 7 months ago

The entire field of chemistry summarised in 12mins from simple atoms to the molecules that keep you alive.

#chemistry #DomainOfScience

If you would like to buy a poster of this map, they are available here: https://www.redbubble.com/peop....le/dominicwalliman/w

I have also made a version available for educational use which you can find here: https://flic.kr/p/UBS4mf
and a widescreen version: https://flic.kr/p/UNA1LW

Errata and notes:
1. I got the Oxidising Agent and the Reducing Agent the wrong way around! Sodium is the Reducing agent and Chlorine is the Oxidising agent. My confusion was that when a sodium atom looses an electron it becomes oxidised, so in my simple brain, I called it the oxidising agent. That is wrong because the agent that oxidises the sodium is the chlorine atom and so the labels are the wrong way around. Doh!
2. I drew the hydrogen H2 molecule with a double bond but it should be a single bond because they are bonded with a single covalent bond.
3. Where I have drawn carbon dioxide, the carbon should have a double bond to each of the oxygens.
4. Apparently Feynman diagrams are not that useful for theoretical chemistry, so perhaps that wasn't the best choice for the illustration. The feedback in the comments from a real theoretical chemist is "All we deal with is shuffling around electrons, but many many many electrons, so a Feynman diagram would need to be huge but at the same time would be very very repetitive."
5. In analytical chemistry, I should have called it distillation rather than precipitation.
6. My definition of organic chemistry being about ‘life’ is not very good. I should have said that organic chemistry looks at compounds that contain carbon. But there are some compounds in inorganic chemistry that also contain carbon, like carbon dioxide so I guess I'd also have to state that inorganic chemistry is almost everything else.
7. I said that fuels are inorganic chemistry which is misleading when I drew a car next to it. My understanding is that there are inorganic fuels that don't contain carbon, but obviously all the fuels we are familiar with are organic. I thought a picture of a car would tie a few things together elegantly, but it ended up giving the wrong impression. That’s okay, I’m still learning! :D
8. In inorganic chemistry, I should have stated that all natural minerals fall under inorganic chemistry so as not to be misleading, otherwise you might go way thinking that only man-made substances fall under inorganic chemistry which is not true. I said that 'a lot of the inorganic compounds that are studied are man-made' meaning that the cutting edge of research is mostly man-made substances.
9. Apparently water is not the most inflammable substance. I thought it was so that is interesting.
10. In the bonding section, hydrogen bonding and van der waals forces are technically inter molecular forces.

Here are some of the references I used for this video if you’d like to dig a little deeper
https://en.wikipedia.org/wiki/Chemistry
https://en.wikipedia.org/wiki/Outline_of_chemistry
https://www.uwlax.edu/chemistr....y-and-biochemistry/s
https://www.khanacademy.org/science/chemistry
https://www.cancerquest.org/ca....ncer-biology/biologi
Early smelting:
http://ispatguru.com/evolution....-of-blast-furnace-ir
Categorisation of reactions
http://www2.ucdsb.on.ca/tiss/s....tretton/chem1/stoich

Thanks so much to my supporters on Patreon. If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much. https://www.patreon.com/domainofscience

Frontiers of Space: http://nobrow.net/shop/profess....or-astro-cats-fronti
Atomic Adventure: http://nobrow.net/shop/profess....or-astro-cats-atomic
Intergalactic Activity Book: http://nobrow.net/shop/profess....or-astro-cats-interg
Solar System App: http://www.minilabstudios.com/....apps/professor-astro

Find me on twitter, instagram, and my website:
http://dominicwalliman.com
https://twitter.com/DominicWalliman
https://www.instagram.com/dominicwalliman
https://www.facebook.com/dominicwalliman