Solving Systems of Equations... Substitution Method (NancyPi)
MIT grad shows how to use the substitution method to solve a system of linear equations (aka. simultaneous equations). To skip ahead: 1) For a BASIC SUBSTITUTION example, skip to time 0:19. 2) For an example where it's TRICKIER to solve and also involves FRACTIONS, skip to 08:17. and P.S.) For WEIRDER-LOOKING DIFFERENT FORMS of systems, for which you can still use substitution, skip to 16:46. Nancy formerly of MathBFF explains the steps.
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For how to solve a system of linear equations with the ELIMINATION METHOD, jump to: • Solving Systems of Equ...
What does it mean to solve a system of equations using the SUBSTITUTION METHOD? It means to solve for the x and y values that make both equations true, using the substitution method. Substitution is just one way of solving (elimination is another way). Here are the THREE STEPS you can always follow:
STEP 1) First, solve for x or y in either of the two equations in the system (get x or y alone on one side). It doesn't matter which equation you use first, and it doesn't matter whether you get x alone first or y alone first. You can pick whatever looks easiest to solve for in the system.
STEP 2) Then, take the expression you found for y (or x) and plug it into the other equation you haven't used yet. For instance, if you got y alone in the first step, take that expression for y and plug it into, or substitute it into, the variable y in the other original equation in the system. Then, simplify the expression by distributing to open up the parentheses (using the distributive property) and combining like terms. Solve for the unknown variable in this equation.
STEP 3) Finally, once you solve and get an actual number for a variable, you can take that number and plug it back into either original equation in the system and then simplify and solve for the other variable. This (x,y) pair is your solution.
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've 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: nancypi.com
Пікірлер: 875
Bruh, she explained something that ive been struggling to understand for years. She taught me three years worth of math class in under 20 minutes and I actually understand now-
@josiahjoseph3025
2 жыл бұрын
True
@BReWeDKnOwLeDGe
2 жыл бұрын
It’s because she’s hot and your paying attention and your most likely.
@adudewithquestionabletaste4851
2 жыл бұрын
well no
@Regular_Decorated_Emergency
2 жыл бұрын
8th grade honors math here, struggling. She is saving my life. 😭😭😭😭
@princessnoelleysulat1294
2 жыл бұрын
@@Regular_Decorated_Emergency omgg sameee
Math: exists My brain: *explosion*
@stanzinzangpo1035
3 жыл бұрын
Mee too
@silentizer4612
3 жыл бұрын
haaaa
@infamousdrin_
3 жыл бұрын
It’s honestly not hard it’s you making yourself think it impossible and it pretty difficult but once you practice and get the concept down it pretty easy.
@apurwa4672
3 жыл бұрын
Bro maths is not that hard. You need to learn all those formulas and understand the concept
Wow, an instructor that tackles the tough cases (which are always on the homework, but never in the examples). You instruction is a breath of fresh air!
@vanessa6236
2 жыл бұрын
Omg riiiight never on practice you take a test and then bam it's there like wth. Why didn't they show this to me in practice. 🙄
@avvieowo6340
2 жыл бұрын
So truee
@victoriamorin9770
2 жыл бұрын
lmao this is so true. Literally just had that happen to me on a test
@madblox252
10 ай бұрын
🤨
I literally had a panic attack because I have a test tomorrow on this and I just thought that I was dumb for not understanding what my teacher was saying but now I know that its his fault for teaching it in a bad way. the way you teach is very calming and reassuring and that helped me understand this super well so thank you so much
@victoriamorin9770
2 жыл бұрын
lmao same tho. I do online so i only have the lesson to try and learn from and if i need help i have to set up a call with my teacher so it makes it harder to get help
im not even paying attention im just amazed on how she can write pretty backwards and also trying to figure out what shes writing on maybe on glass? thin air? idk
@onlinefool9931
4 жыл бұрын
editing....
@rustyorlando
4 жыл бұрын
I assume it a piece of glass and a mirror.
@mathisfun8797
3 жыл бұрын
kzread.info/dash/bejne/i6VnvNRsocSbpqg.html
@lenliz2003
3 жыл бұрын
so true
@judynyambura9233
3 жыл бұрын
its quite confusing how she does it
Recognized how hard it is to write backwards......
@a-level88
5 жыл бұрын
Shes not writing backwards, she's just flipping the video so to us it looks like shes writing with left hand, but shes actually writing with her right hand
@VarietzHD
5 жыл бұрын
@@a-level88 ^ lol
@ares2067
5 жыл бұрын
Agreed, but what if she is also right hand dominant? Even more impressive.
@justinsumba3510
5 жыл бұрын
Oh yeah yeah
@bonbon2235
5 жыл бұрын
she might be using a mirror which would flip the whole image
Nancy is my favorite math tutor on YT! 😭😭😭😭 Thank you so much! You are even better than Brian McLogan!
"You don't have to like math but you can like my video" I don't like math but I have liked every NancyPi video I've ever watched because you're always so helpful! I like how you somehow manage to squeeze entire lessons into 20 minute videos without losing me at any point (which is what usually happens with other YT instructors). Thank you and keep making more videos ❤
Beauty and brain in one place. A rare sight indeed. Thanks Nancy
@dilipmutkundu15
4 жыл бұрын
Perfect sentence😊
OMG, Thank the heavens for Nancy Pi!!! You have restored my faith in math! I love it and was feeling very discouraged because I wasn't getting it. Watching your clear, step by step videos has brought it all back for me. Thank you Nancy!!
The COrona virus is upon us and I'm watching this video, it was really helpful! thanks!
@niharikka6342
4 жыл бұрын
Are you in class 10th tell me😊
@lenliz2003
3 жыл бұрын
Ya I agree because I am in grade 7 and I still struggle
@lollol-rn9kp
3 жыл бұрын
im in 10th grade :p
@dngosama
3 жыл бұрын
Still not done
@dngosama
3 жыл бұрын
Still not done from future
Bruh this is the 3rd time I come back to this Video in the last 4 years Nancy u are a lifesaver
You have, in a single video, shared your knowledge, clearly and with great patience, for the betterment of my incredibly frustrated and challenged mind! I am forever grateful for your talent and thoughtfulness; please keep making videos ( algebra specifically). I “get-it” now, thank you!
THANK YOU! I've watched several videos by other teachers and professors and none of them wrote out the steps, like you have here right in the beginning - SO helpful!
I thought I'd never be able to do these. This was extremely helpful!
tysm its hard to learn in online school and this is the only video that truly helped :)
Almost 9years later since i studied maths in school, this video for the 1st time in my life explained solving equations so lucidly that i can't thank you enough Nancy
damn she is lefty and is writting backwards!!!
@nidoruzi
4 жыл бұрын
lmao it’s flipped. she’s not writing backwards
@mathisfun8797
3 жыл бұрын
kzread.info/dash/bejne/i6VnvNRsocSbpqg.html
@andrewmcnamee5454
3 жыл бұрын
its just glass bro
@norah496
3 жыл бұрын
@@andrewmcnamee5454 ah me so dumb lol
Can I just say this video is the most helpful one out there! Love it!
giiiiiirl you helped so much, thanks!!!
@dilipmutkundu15
4 жыл бұрын
True
@vikasrai8508
4 жыл бұрын
Hii
I wish you were my teacher in school. Thank you so much🙏You helped me more than you know.
Thank you so much for taking your time to help others this video helped me out so much. Now I feel I can be successful in college algebra at jersey college.
THIS WAS SO HELPFUL!! YOU CLEARLY EXPLAINED WHAT TO DO WHILST THE TEACHER TOOK A WHOLE LESSON
I spent the past week struggling so hard with this and now I understand so quickly. I literally love you thank you so much, hopefully I won't fail another quiz!
TMR is my final and this is the only thing I struggle on.. so I’m so thankful I found this video you teach better than my teacher
Coming out with all these videos before my finals bless you
@cj_combo5442
5 жыл бұрын
Are u in college doing this? Or highschool
@potato7688
5 жыл бұрын
@@krystianmurdzek6877 same
Thank you for this, doing math assignments that are late because I didn’t know how to do it, but thanks to you I do now❤️
I love how u lay things out!
I knew all my confusion would be gone after watching this video, and I wasn’t wrong. Thanks for helping again☺️been watching those videos for almost four years now, saved my ass countless times
@animestudios9078
2 жыл бұрын
Good teacher
@animestudios9078
2 жыл бұрын
Good
This is literally the one thing that i literally cannot do!! And you helped so much you explain everything very intricately and you make it simple. Thank you so much i fr had to do this hw over 6 times
I want to thank you. I have been struggling with a teacher that doesn't want to teach and you saved my butt.
This is great and so helpful! Thank you for making this :)
Hi! I am in year 9, and I was blocked in these topics for a while. I didn't really get closer but now, as I watched this video, it helped me a lot. SO thank you. I love the way u explain, you are very clear with what you wanna say and speak English in a very nice way. Thank you.
Thank you Nancy, my professor went over so fast in class so I didn’t get it but your explanation is really helpful!
Thanks found it very helpful. Wrote it down step by step. back in school at 56 so I have forgotten so much and felt overwhelmed and anxious. I've always hated math so many thanks
@Regular_Decorated_Emergency
2 жыл бұрын
Great for you!!
You make the equations easy to solve. Well spoken, clearly defined problems and solutions. My ERAU instructor linked us to this video, very pleased. Thank you!
i love the way you teach nancypi
Finally, you are an angel sent from above by the math gods. Thank you very much..
Thank you Nancy! I know that this might be over 2 years too late but your videos really helped me out because later in the school year I will be taking my EOC!
dude i sat in a 2 hour class tryna learn this, and i just learned it in under 20 minutes, this is why i hate school. thankfully i can find vidoes like these
Thank you so much! I understood your video, unlike my math class at times! :)
Nancy, you rock. Thanks for doing this!! BIG help
You helped me with math in high school and now in college haha. Thank you! girl you are heaven sent.
2 years from the future thank you so much ❤
Everyone: pays attention to the math that she's explaining Me: Trying to figure out how she's writing backwards so neatly
@Eray2007
3 жыл бұрын
Not really m8 its the other way round
OH MY GOD THANK YOU SO MUCH BEEN STUCK FOR SUCH A LONG TIME!!!!
Nancy, I loved your video because you are very detailed in your teaching. Awesome!
Generally this demonstrates the technic of substitution for, may be, more complicated sets of linear equations. With this easy set, it would have been easier multiplying the first equation by 4 and add the 2nd to it, eliminating Y in order to get X. (With 14 to be the common denominator of 2 and 7 we could multiply the 1st e. by 7 and the 2nd e. by 2, in order to get rid of X and get the value of Y, by subtracting the 2nd e. from the 1st. e.).
I missed the lessons by the time my mathematics teacher was explaining this,but am glad that she has really helped me.
This time, I really had to pay attention, and Nancy says it plain and simple in a way I can easily grasp it. Thanks
I FINALLY UNDERSTAND! THANK YOU NANCYYYY
woah! this what i was looking for thanx this helped me a lot
All of ur video is very helping me in my math. Last month, I got 86% for my mark. Thanks
I LOVE THE WAY YOUR DOING NANCY ..YOUR HELPING SO MUCH.. THANK YOU SO MUCH.. PLS DO MORE VIDEOS..
@Asif-jt2hk
4 жыл бұрын
You're*
@grxgr9213
4 жыл бұрын
@@Asif-jt2hk grammar police lmao
Your video helped me a lot. Thank you so much!
Love this channel, thank you so much
@Moeyyclips
5 жыл бұрын
aye
Hi Nancy! I found that this works a little easier and w/o dealing with fractions. multiply the bottom equation by 2 and u will see it works out very nicely. I always take the easiest term that will cancel out the top/bottom term to eliminate x/y. In this case u got the best of both. 😊
@jin-jq5np
Жыл бұрын
thank you so much i love you
y'all telling me she was writing backwords?? NOW that is true commitment! ANd thx your helped me study for my finals thx thx thx.
Thank god, finally a pretty math teacher and the name Nancy pi perfect. God bless you Nancy.
not even 2 minutes in and I already know exactly what to do! thanks a lot this reallly helped :D
Thoroughly enjoyed your video
This helped so much thank you!!
Best tutorial ever. Thanks Nancy
Thankyou so much. This was so helpful
love your work
Thank youuuuu so muchh for your helpful vid....... lately Im struggling solving these thingss.... but now its really easy for mee..... thanks again♥️
Thanks for your slow and cincise explanation your just the best math tutor love you all the way from Papua New Guinea may God bless you for your heart of teaching
Thanks for this. You only realise how much of this stuff you've forgotten when you need to use it.
Thanx a mill, you made it so simple and easy to understand!!
Really loved this it was so useful Thank you
Thanks Nancy! you rock!
Watched this to complete my math assignment. Thank you for helping!
Thank you for all the help
Thank you. I really appreciate your help
Thank you for bringing up these special cases 🙏 I was tearing my hair out yesterday trying to solve similar problems. Great explanation 👍
Nobody: Math:iNfInItLeY mAnY sOlUtIoNs
@nightstech7499
3 жыл бұрын
Infinitely many solutions = Infinite number of explosions in my brain, makes sense
@MathProfessorKyleMartin
2 жыл бұрын
If you need an I.M.S. I just made a video about it!
Omg thank you girl😭 I needed this!! Thank you a million times you’re a legend!!
@silver_kage3154
4 жыл бұрын
Next upload?
@iimavyyy
4 жыл бұрын
my momsphone next upload what do you mean?😂
@silver_kage3154
4 жыл бұрын
@@iimavyyy 2 weeks without uploading
@iimavyyy
4 жыл бұрын
my momsphone YEah I’m uploading tomorrow 😂 because I’ve been busy with college :(
@silver_kage3154
4 жыл бұрын
@@iimavyyy oh dam
Hi Nancy, excellent explanation, and very clear. Thank you so much. God bless you.
Thank you so much It help Me a lot nancy
this was so helpful thank you so much!!
Thank you! I have a test on friday and this helped. My teacher doesn't really know how to use the online learning software.
I'm taking a math class that I should have taken in high school and this was very helpful. Thank You. Also, my ADHD could not help but focus on the fact that you are a fellow lefty and you have to write backwards. Great quality video! Subscribed!
@jin-jq5np
Жыл бұрын
me too 🥲
Nice. Steady paced and easy to follow. Keep encouraging.
I remember linear algebra. That was some really bizarre but cool mathematics. Have you ever set up a system of equations and then converted the matrix into echelon form obtaining the answers on the right side of the equals sign? I got fast at that once, but I think I'm a little out of practice. Once, I also wrote a very cool computer programming routine that worked like a charm in most situations. Imagine a program where all you have to do is put in the known variables, and it automatically solves for the unknowns. This is a science all of its own!
I saw this video as was scrolling through the internet for systems of equations, why because I was failing my 7 grade algebra class I saw the video a good 3 times and I turned into a calculator. thank you so much. (T_*) thank you
I have a math test coming up this Tuesday and this video was really helpful. I am leaving a like...
Omg thank you so much I have a test tomorrow and you are the only person on KZread I actually understand
@lucianacantu8901
5 жыл бұрын
Super grateful!!
Thnx a bunch, this video helped alot 🥰😘
Thank you so much for this!!! SUBSCRIBED 💖
INFINATELY MANY SOLUTIONS!!!!! THANK YOU VERY MUCH
This helps alot, thank you.
Thank you so much this really helped me!
Thank you so much for this😁 it really helped! I got the same answer as when I used the method elimination💜💜
Great work!
You probably won't see this comment but I want you to know that I have been struggling with these and so I watched this video. I got the correct answer thanks to you and your slow pace at which you explained each step. So thank you so much. You helped out a struggling student:)
I love you continue teaching us how to solve the problem of equation you teach us with much love
Where were you when I was taking HS Algebra? You have a pleasant demeanor and your students should be grateful.
Thank you for the help, I am a new subscriber from now on!
@ahkeelmccooty5631
4 жыл бұрын
2020 person watching a 2018 vid :]
Understood this in just a couple of minutes thanks it was very helpful 👍👏👏
Woahh u saved my lifeeee , I have my maths exam tomorrow and now I'll GE good grades inshallah