Solving Systems of Equations... Elimination Method (NancyPi)

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: • Solving Systems of Equ...
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".
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[@kathrynhooper2351]

This was so helpful. I had no idea how to do this as all the other videos were unclear and messy. Not only this they didn't use equations that needed either 1 or both sides to be multiplied. Thanks this was the last part I needed for my math exam tomorrow (technically today as I have been up all night into the morning studying... oops).

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I've been using your video on the elimination method for System of Equations, with my fifth graders. You explain the process beautifully. They are understanding how to find the solutions.

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i saw Nancy 2 years ago when i had to help one of my kids with quadratic equations she was the only instructor that explained in a way that i understood now i am back for the linear equations for another one of my kids thanks Nancy

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Failed my test had to retake an this helped alot

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How much you got on your re-take tho???

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Only 5 minutes and I can see easily how to do this properly. My teacher always forgets something and then we have to go back and change it then the correct part of what I learned is only partially correct. And relearn the whole problem. After that when I know part of what I’ve done is correct another student has to tell her that she’s wrong again about something they noticed. This causes so much doubt in the student’s skill they already had. This has been happening daily since August. I can’t think of one day this teacher didn’t make a big teaching mistake...even on quizzes and chapter test. 😞 Seems like she’s only doing the problems for herself and not teaching.

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in that case, your teacher needs a check up on her job. Seriously.

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Thats a horrible teacher then

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This made so much more sense than any of the other videos I watched , thank you so much

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[@malava9822]

I understand Solving Systems of Equations at 19:40 only in one day and my teacher took 3 weeks and I didn't understand anything. thank you sooo much u saved me

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Thanks helping me understand elimination helped a lot continue the videos thx!!!

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We've missed you Nancy. I have a Maths exam tomorrow. I'm actually looking forward to it.

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Mr.Mister how'd it go?

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My math teacher gave this to me, and I haven't watched this one yet, but the substitution method one helped me so much. Thanks!

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You are a savior. Your "Hey, it's okay!" demeanor and explanations of how it's okay to do equations differently have completely made me remember how to do things; you are carrying me through college :) thank you. You deserve more outreach!

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Thank you best teacher out here for reaaaal was struggling before watching your videos 😂

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Me too

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Thank you Nancy ! For making this videos 🙏

[@SlinkyVibe]

Omg thank you so much for this video. It's almost like the fog lifted in 19 mins. You taught what most college teachers don't. Its the in between steps that they should be teaching. They forget that most of their students are not straight out of high school that remember all the techniques. this made this so much simpler than I could ever imagine. Thank you so much. Your doing gods work lol .

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They don't hold your hand in college. Find a capable study partner if you can.

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Absolutely fantastic video. Makes the solution of equations very easy to comprehend. Thank you!

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She's not black.

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I have been trying to understand this for 4 months now and i just learned it tysm ❤❤❤

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I learned this equation in 20 minutes with you compared to my 40 minutes learning

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hey NANCY you are LEGEND My teacher explained till 1hr 30 mins but i didn't understood. When I saw your video i got this in just 10 mins........

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Awesome! Thanks, Nancy!!

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Wow I learned more from 20 min of you then all semester from my teacher 😂

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“You don’t have to like math but you can like my video!”-🤣😂🤣😂 & for the record I did not like it, I loved it!!❤️

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I just flunked an online college Algebra class because the teacher just made us watch videos and taught nothing. Her videos, as an example, only showed your first set of easy to solve equations. However, the final had equation sets like your last example. Thank you, because this now makes sense.

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Most college teachers are horrible instructors. That's why students skip classes and study on their own.

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Magical

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Meteora Lord 😂😂

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Kpop group?!

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Thank u because the way my teacher taught the multiplication part pissed me off

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Now for real this just help me pass one of my tests thank you

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Taking my ASVAB and just trying to brush up on my Mathematics and this was super duper helpful!

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Thanks so much Nancy for helping me understand

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WHY DID THEY TEACH ME IN THE HARDEST WAY POSSIBLE! I have a test tomorrow and this really helps! Thank you so much! 🤗

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I learned so much here. THANK YOU!

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I'm still trying to figure out how she writes on the other side

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If you look closely at a photo of Nancy (other than in a video) the explanation should be there.

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It’s mirrored

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So am i

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@@jayboco3446 Or she is writing ON a mirror?

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*Dislikers are school teachers*

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Thank you! In school it took more than an hour to teach this and I still didn't understand, this video taught me in 6 mins!

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How the hell are you writing backwards lol

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shes normally writing but just mirrors the video

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@@tokyuu8342 She could be writing on a mirror!