Algebra Trick to save you time (Algebra Tricks)
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- Опубліковано 5 лип 2024
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Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.
Make sure you only do this with LINEAR systems of equations.
AND check out my MATH TRICKS playlist!
ua-cam.com/video/Ks-wwYpS20Y/v-deo.html
I think it's Kramer's rule..ohh u already mentioned there....on calc u can get d ans
superb
@BriTheMathGuy hi I want to know how I can find x and y
For solving liner equation for more then more than 2 equations using the Kramers rule?
I was searching for that video you mentioned in this video, But i can't find it.
Ah does this work for 3 equations? I forgot about this stuff
Algebra, please stop asking us to find your X, she is never coming back and don’t ask Y
:)
Wow this is perfect
😂😂😂
Haha
My friend posted that lol
I took the risk on doing this technique in our Calculus exam, and it saved me a lot of time. I practiced your technique, sir. Afterwards, I used the same old process (Elimination-Subtitution) and yeah, I got the same answer.
Elim and sub take way too much of my time, I use this method first and If I have any time left I go back and try either to verify my answer.
Obviously, it's based on a mathematical theorem. Cramer's rule, which is something you learn pretty quickly in a linear algebra class, as he mentioned. The only thing that was not mentioned, however, is that if det(A)=0, you cannot apply Cramer's rule, where A is the coefficient matrix of the linear system. (That is, the matrix is nonsingular and the linear map represented by the matrix is an isomorphism.)
That would mean that there are cases wherein this method would not work. In fact, there are infinitely many linear systems that this trick would not work on. Also, he did not mention that the system of equations must be strictly linear.
@@PubicGore he did
I think the only issue with this technique is maths tests tend to mark on method rather than answer and even though this law can be valid and has proof attached to it. It isn't mentioned in the work or even stated what Kramer's law is. ( I know he says it but it isn't in the actual writing) so as a result it is unclear whether you had used proper logic to work out the equation or had found the answer randomly and made up an equation to try and show how you got the answer. It seems unlikely but I have done this my GCSEs years ago. I accidentally found the answer doing no work and made up a solution. In this video he does have a quick method but I'm reality he would need to write a lot more for it to be a viable answer in exams. I had a lecturer which would have given me a single mark for answering a question this way so be careful
@@PubicGore I learned Cramer's Rule in my hs Algebra class lmao
I really hate math because I feel like my future depends on it and if I dont pass I won't graduate it puts me a lot of pressure.
Key is to identify what you're having trouble with and attacking that weakness head on.
@@535 i guess i have to redo math
I hate maths
Maths needed to graduate
That's not a theory that's a fact
Yeah math takes so much time and effort but in the end it's slightly worth it lol
During the pandemic I've decided to get into Math as a hobby. I've always wanted to just never had the time. This is an awesome trick. Thanks for sharing. Anybody have any suggestions. I'm building up to Physics.
I want your motivation 😭
That's great to hear! Thanks for watching and commenting.
@@namkoofiles5267 i want ittooo
Congratulations! Me too. I joined World Science U. Some fantastic physics classes for free . I'm here because I need to brush up on my algebra.
Watch the Feynman Lectures on UA-cam, they are great.
did he just solve an equation, backwards? wow
I thought so too
Video editing is powerful :)
@Angus beef I also doubted I could do that but I figured it out in my own around 2 mins in the video. Simple but powerful trick
°^°
0.0
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In India, we are taught this like a formula.
This method is called the cross-multiplication method. The formula goes like this.
For the standard form of system of equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0,
x/b1c2-b2c1 = y/c1a2-c2a1 = 1/a1b2-a2b1
This method is not exact to the method you said, but it is indeed similar...
My reactions after seeing all these number: Koi mujhe pakro mereko chakkar arahe hae
yes, it is in syllabus of class 10th
it directly gives u the value of x and y, I learnt it this year only xD
But in this method there is more chance that you will do a mistake and it takes
comparatively more time
@@ggman4544 If you see closely, you can very well take out the x and y in terms of the coefficients of the equation. It is just simple to list the values of the coefficients substitute and solve, no hurdles.!
Does he ever forget there's glass in front of him and he accidentally bumps his head on it
toffee. He’s in a cage but we aren’t supposed to know
Now that you said that, is he writing backwards? (I'm distracted lol)
@Yared Delva they give me plenty of food and water, so I'm doing alright.
I don't think I ever bumped the glass, but I'm pretty sure I hit my head on the microphone out of frame hanging above me.
@@BriTheMathGuy a small price to pay for salvation
this is why i miss school i need to learn and virtial learning isnt helping me with math
FRR!! SAME!!
Yes virtual doesn’t teach well but majority of teachers don’t know this trick so either way you most likely won’t be taught this in school Math teachers don’t like cheap tricks in math for some reason
its not the online learning fault ur just not focusing💀
For anyone curious:
You can have this written down as Ax + By = C, and also Dx + Ey = F as the second equation.
If you isolate y in the first equation, you’ll end up with this equation: y = (C - Ax)/B
Now, if you plug that value of y in the second equation, you take these steps:
Dx + E[(C - Ax)/B] = F
Dx + (EC - EAx)/B = F
(DBx + EC - EAx)/B = F
DBx - EAx + EC = FB
(DB - EA)x + EC = FB
(DB - EA)x = FB - EC
x = (FB - EC)/(DB - EA)
x = (BF - EC)/(DB - AE)
And that’s exactly what’s done here
.
Thanks!
Thanks man
I love looking at this shit before I even have a full grasp of what it entails and admiring how unnecessarily complicated it seems
Bro can a ask if I have any question in maths cuz you seem like you exactly know what math is.
This seems like more rules to memorize without understanding why it works. I dont think its worth memorizing this for such a small use case. I would rather do a tiny bit more work and be more confident in my answer. But cool trick nevertheless.
Prove it to yourself by solving with the substitute technique the set of equations :
ax + by = m
cx + dy = n
You'll realise you'll end up with formulas for x and y that are exactly the ones he uses in the video.
@Umang Ravaiya I kinda hate cross multiplication method ngl
It is a cool trick but you hit the allegorical nail on the proverbial head that it's just a mindless automaton method to memorize, it's gets to the answer but provides zero insight. Brian really disappointed me here.
@@JamesWylde we dont care about insight, e wanna get the questions done fast in an exam
@@sokatunier8607 The question is not if it's true. Yes, of course it is. But you DO have to remember the steps. The normal methods involve no memory work. If your memory is great, bully you. My memory is awful but I always did best at Maths because I could figure out most of it on the back of a very few remembered facts. And if you're fast with calculations, it takes you very little time to work out simultaneous equations in the normal way.
This is called Cross multiplication method and very helpful when coefficients are small enough to multiply easily
This guy...right here...is an absolute legend.Thanks alot for showing this method,I'll make sure I forward this to my friends and teachers!
Oh my gosh, thank you so so much. I am from Singapore and I’m secondary 2 or grade 8, the whole textbook was algebra, and you helped me so much, oh my gosh I can’t thank you enough!
I figured this out completely on my own when I was 18. I was going through my College Algebra book and was obsessed with finding shortcuts to solve things faster.
Thank you so much Brian. Found this video last minute before my tests in Maths. It is very useful and I definetely subscribed. Thank you so much, Really appreciate it.
Glad it helped!
found it rn,2 days later my math exam,lets goo
im crying you are so amazing, ever since grade 7 i have had terrible teachers so i struggled with basics and now i am in gr 11 and i have came so far with you videos .
This is amazing how I learnt how to solve an equation In less than 1 min
Replying to comments a year after, instant subscribe.
I really appreciate it!
Wow I really enjoyed this video. I actually just finished linear algebra and solving systems of equations was a lot easier in matrix form. I wish I would have known about this back when I took algebra in high school. Love your videos. Keep up the good work.
Thanks, It really helped me a lot . Teaching + Explanation + Opposite writing = 💯 out of 💯 👍👍👍👍
I still can't comprehend because i'm stupid and i lack discipline
I was taught about it since I was in primary (elementary) school. But I never know its name until I got into university where I took up Math as my major. It felt incredible at that point to finally understand the mechanism behind this formula. I will not disclose its name but let your curiosity run its course if you so wish
It's called method of cross multiplication.. it's actually done in a bit of a different way as we are taught in 10th standard here in India..
U probably won't see this but this helped me soo much I've been really struggling on algebra because most things my teacher says make no sense so thank u
this is awesome how you do it so fast! but i just started so I didn't understand much lol btw i subscribed
Thanks for subbing!
I just realized this guy is doing the equations backwards.
Major respect for this guy he is the maths teacher we needed.
Yeah
He video edited
I love your videos. Could you please share some tips on how to make Real Analysis a bit easier?
i'am loving this trick!!!! shouldn't learn this sooner!!
3:00 Lol I remember my buddy Cramer in Linear Algebra.
What a cool use of determinants
You make it easier, Thanks for your videos 💕💖
You’re very welcome. Thank you for the support!
To tell this more simply this is the x/() =-y/() =1/() trick
In those brackets the coefficients of other than the variable you're writing it below.
watching it on quarantine at may 2020, subscribed. you're my life saver. i hope i could do this in 7th grade
Glad to help!
7th grade? im an 11th grader just now doing this lmao
I'm in 8th grade but getting ready for freshman year.
I'm in 7th grade learning this stuff😭✋not understanding a thing-
@@BriTheMathGuy wait- then no one wonder I failed my math class in fifth grade cause we were literally doing this
I think using the original order of calculating what would be the "determinate"( instead of reversing the order) is yet easier in terms of visualizing the simple cross-multiplication involved. In any case, just another tool I'll put in my tutoring toolbox. One of my favorites is for fiddling the turning points (relative max and min) for a cubic function. We all know the quadratic formula, well the formula for the X-values of the turning points of the cubic AX^3+BX^2+CX+D is practically the same. Instead of B^2-4AC inside the root, it's B^2-3AC and instead of dividing by2A, divide by 3A. If "A' is positive, the smaller X belongs to the relative MAXIMUM and the larger X belongs to the relative MINIMUM. If "A" is negative, vice versa. This formula gives EXACT answers instead of the approximations found by graphing on a graphing calculator. It's pretty cool. Cheers. And LOVE your channel!
this is SUPER MINDBLOWING AND IM IN GRADE 5 THANK YOU BRIAN THANK YOU
My eoc is tomorrow and I think I'm gonna fail, I dont get why they gave us testing this year with covid 😭
SAME
SAME MINE IS ALSO TMMR
mines today lol
I’m afraid that I might fail
mine is today and i feel like i haven’t learned anything all year
Thanks for all the tricks :D. I love all your tricks :)
Happy to hear that!
Basic idea of algebra, but very essential ones. Learnt a lot from this video. The way you present the lesson make it looked so easy. The explanation also very smooth and easy to follow. so happy find this video. Thank you very much.
This helped me alot, Thank you so much!
Glad it helped!
I love this man soooooooo much right now. This is so freaking SIMPLE!!! How many videos have I watched and NONE of them put it so simply. This will save me a lot of time on my math homework.
Glad to hear it! Have a great day and thanks for watching.
I thought about falling face forward in my notebook but I was like “Really you know you can do way better than just give up”, found your video!
this video was such a big help! thank you so much!!
Magical
Having already done solving simultaneous equations using matrices - literally, explicitly using the matrices - I immediately went “so he’s doing the matrix stuff, just implicitly” before you even said. Still a cool trick to know.
Amazing first time exposure with this guy
Thank you wery mach !!!!! This wideo really saved my time !
That's amazing bruh. Thank you so much for info !! :D
Happy to help!
Hi Brian your video are very useful I have subscribed thanks for all the tip and tricks it really helped me in me exams
Great to hear!
Do y'all realize he has to write opposite so we can see it lol
Video editing is powerful :)
@@BriTheMathGuy hahaha
@@BriTheMathGuy Ah yes, mirror effect
btw great video
You’re sarcastic, right?
Dude... how did you do this video. Even if it’s reversed image or mirroring editing option. You would half to be behind a piece of glass or something transparent writing on the other side but even then if you reverse the image or mirror is it the right or the left hand being used
Thank you King! Respect from Indonesia 👍
That's pretty cool. I never thought to cross multiply like that.
Seriously, I didn't understand anything
Guess I forgot everything from highschool
Is this for beginners? BC I think I should start worrying about myself lol
Do u have lessons for complete beginners on Algebra
I’m facing same.i am freaking out .i thought am brilliant lol
Wow I’m so lost! Since 07’ wow!!
You better start fam, you won’t get to where you want in life if you can’t find x. Better late than never
@@cosmic4588 Sorry bro but certain things you dont need to find x
Do you need College Algebra Credit? I got 97% as a final grade and was able to transfer the credit to my university contact me got more info Secretstocollege@gmail.com
Awesome tricks. Thanks so much. I enjoy this video.
Somebody give this man a medal
So I'm not great at math but I remember when I was little my dad taught me all about matrices and determinants for no reason and so this trick made a little more sense when you told it.
When I found out about cramers method and also inverting matrices through cofactors I felt like I found something I was missing for so long in my other classes.
I also think it's interesting that if you divide by 0, there's either no solution or infinitely many solutions through the invertible matrix theorem.
I just subscribed. Thanks so much
Seriously! I just subscribed!
This is called the cross multiplication method. It's super common in India. There's a whole exercise based on this method in 10th grade textbook
Your awesome. I am a newbie. Does this method work all the time? Second question, do you have more tricks? Thank you
What's great about math is that it always works every time (provided you meet the conditions of the theorem, situation, and do all the steps correctly). I do have a few more tricks around my channel, mostly concerned with calculus. Best of luck!
We were taught this in elementary school, it's called CROSS MULTIPLICATION METHOD. We got 4 methods:-
1. Substitution method where we find the value of one variable and substitute it in the other equation.
2. Elimination method where we try to eliminate one of the variables by substracting, dividing, adding, or multiplying the equation. (My favorite)
3. Shifting method where we find the value of one particular variable (say x) from both the equation and then equate it with each other and solve for it.
4. Cross Multiplication method
The thing is that you just showed it directly but we had to do certain steps before that.
Nice Video BTW
Are u Indian?
This is in 10th cbse as well
@@jhingalala_chimpui Ya am Indian but ICSE class 9
This is amazing!
I mean I guess it could be faster, but if you're fast at solving with elimination, it could work better. Either way, it's a neat trick to know and I will use it sometimes
Question. How do you know which ones to myltiply first, and which ones to minus, like which equation to put at top
Thank you so much for this!!!!!
You're so welcome!
Thanks for the great help
You’re quite welcome. Have a great day!
I guess that's a kind of cross multiplication method that we as well as our teachers used to skip in our schools:)
This had really help me
Glad to hear it!
holy freak this actually saved me so much time, thank you
Love this!
Wow thanks i love this im now perfect at algebra thank you sir!
Happy to help!
@@BriTheMathGuy hi handsome Nerd with thousand of IQ
Thanks 😘 bro...It was really needed by me....
Happy to help!
This would've actually been helpful if UA-cam recommended this to me yesterday when I had my math test
Your the MATH man, best of all
Seems more confusing than (1) multiply top equation by 2, giving 2x+4y=22, (2) subtract eq 2 from eq 1, so 2x+4y-(2x+y)=22-10. 2x cancels out, so 3y=12, y=4.
Pls include the 3 equations trick i love learn that pls
*when your the first guy to reply* me: uhm..
Just wanna say thank u for this trick it's litteraly sooo helpful TT
Happy to help!
That was help to me thanks
Not me watching this before a test:
Same 😂
As a math teacher for 42 years I must say WOW! This is such a neat method that should be added to the other ways a system of 2 linear equations can be solved. What is needed is an appropriate name for this method.
How about the XXX method or Crossing the System or ______.
Cheers
It is called cross multiplication method... They r taught to 12 year olds when they r introduced to substitution and elimination
Wow...awesome...really helped me..thanks!
That trick is the short version of Cramer's formula. Neat!
He is pro at this :O
It is just the cross multiplication method of solving equation...taught in class 8-9-10th in India.....he just tell it in a simplified way.....but still great video
yeah i was wondering that. i was taught this in year 9 apparently.
I was taught this is in year 6 and ;-;.
exactly, it is not a trick it is just a memorization of the general formula/method.
yeah this is good but thers marks for formula and steps soo....
THANK YOU!!!!
You're welcome!
I love using Gaussian elimination and I kept thinking of it as a solution for all the systems until the end of the video 😂
This is actually something we are taught along with elimination and substitution, generally referred to as cross multiplication. I never really used this though, because there's a lot of room for error, like you wrote the coefficient of x instead of y, etc. Still, a good method to know 😇
Flawless
Glad you liked it!
Hi, Would you mind if I ask you? Is this trick available to all given problems in algebra? I just wanted to know. Thank you.
Thank you so much.
You're welcome!
This method is taught in schools in India
Infact it is even in the maths book and compulsory to learn < we call it the cross multiplication method here
Yes..anirudh...yeh..to humare liye normal hain!👍😎
Wow!!!
I know right?!
Thank you!
You're welcome!
Excellent!
Nebulous have a wonderful day!
This was a great video really appreciate the technique! What about systems of equations that have no solution?
Such as:
-4x + 8y = 1
and
3x - 6y = 2
I tried using this rule for these equations but when plugging them back into the original equation they do not work.
When using the elimination method the answer ends up being a contradiction with no solution. Would Kramer's rule still be relevant for these types of problems?
There is no solutions for this system so the formula won't work
@@gregorydaude4781 Ah ok good to know thank you.
Simultaneous equation is used to find out the intersection points of two equations, if there are no solutions, that means the two lines does not intersect. In your example, the two equations both have a gradient of 1/2 and that means they are parallel and therefore does not intersect at any point, and hence there is no solution.
This trick is awesome!
Thanks very much!
Comes from Matrices.
I don't advocate teaching these tricks unless people know where it comes from.
The reason is that math should not be about getting the answer quick, but rather proving what the answer is every step of the way.
An answer is no use unless you can show others why it is true.
Its really helpful thank you!
Glad it was helpful!
@@BriTheMathGuy :/)
Nah man thank you so so so much, I spent 5 hours trying to learn how to solve system of equations using matrices and I learned right away how to solve it right after watching your vid.
WTH! What did I just see! Algebra made easy....NO WAY!!!!
Very glad you thought so. Have a great day!
You solved for X in under 30 sec. Granted, the writing and demonstration took up the bulk of the time, not the thinking part of the math. I appreciate a clever math trick as much as the next mathematician, but I solved for X myself using standard substitution method and it seemed easier and took less time for me. Maybe this is due to me being used to doing it that way for over 40 years, but substitution has the additional benefit of understanding the values. The alleged time saver is fun but I believe kids should know why the values are what they are.
This helped me with homework, thank you so much!
Glad it helped!
THANK you, even if it's for doubles, hey- its a HUGE help! It takes SO much time out of equations for X,Y=.