The 4 popular methods of solving a 2x2 system of equations!

[@K2MusicKSquare]

Never learnt or heard of Cramer's Rule before. That's new to me.

[@kevinstreeter6943]

It is part of Linear Algebra where the coefficients are put into a matrix.

[@savitatawade2403]

​@@kevinstreeter6943 in my country, we have no idea what matrices are until we learn precalculus this method was given in our book earlier but got removed for some reason

[@Rey_R_]

When Cramer says "buy", it means "sell" and vice versa.

[@sohailansari07289]

An easier way to remember it is first take a1,a2 b1,b2 and c1,c2 in the format in video. Then for Dx put c1,c2 instead of a1,a2(x coefficients) and for Dy replace b1,b2(y-coefficients). For D just take x and y coefficients(all on LHS). Then x=Dx/D y= Dy/D

[@sohailansari07289]

You can extend this concept to three variables, x, y and z and solve for them similarly by creating a determinant of order 3.

[@AngelesBustamanteM]

Solving systems was one of my favorite parts of maths class 🤩 never knew about the last rule 😱

[@msolec2000]

Well, way back when I was being taught this, they taught me three methods: Equalization, Subtitution, and Reduction. Reduction is what you called Elimination. The Equalization method is the first that I was taught, but never used it unless the question in the test said "solve by equalization" or something, because it is a bit impractical. You had to isolate the same variable in both equations. In your example system you would work out y=(2/3)x-2 and y=-4x+5 (like you did with graphing), then, since both of those are equal to y, you can write (2/3)x-2 = -4x+5 and solve from there algebraically.

[@Caybra]

My preferred method to solve a system of equations (whenever I have a calculator) is to shove that crap into a matrix and convert to rref. It’s really efficient if you’re fast at typing and get the buttons down to muscle memory.

[@ibraheem_Zain]

I also love matrices method it's the best❤❤ 🤫💪

[@savitatawade2403]

​@@ibraheem_Zain🤨

[@박강현-k9k]

Thank you math teacher and Cramer who I have never heard about. This is so fun and entertaining I am making my own problems (knowing x and y value from the beginning) and solving it in the correct order

[@jurajhabek2782]

I love your video man keep going, i love your video on using quadratics in physics for rockets, would love to see some more videos on the matter of using math in real life/implications of math

[@tylerlaceby]

Somehow this got recommended to me. I’m in linear algebra now along with differential equations and some other maths classes. I personally find Cramer rule to be easier to do once you’re used to it. I mean the determinant is sometimes annoying but I make less computation mistakes with that then elimination xD. I love your calculus videos and others. Keep up the great work.

[@bprpmathbasics]

Thank you!

[@crtlallaw]

row echelon form best

[@JubeiKibagamiFez]

I like Cramer's Rule. It's easier to remember.

[@MathNerd1729]

Understandable. I haven't practiced much on Cramer's rule, so I may find it a bit difficult to remember which order the subtractions must go at times. Yet it is quite an elegant method! :)

[@JubeiKibagamiFez]

@@MathNerd1729 I haven't done any of these maths before, so for me, less steps is easier.

[@Faroshkas]

​@MathNerd1729 It comes from matrix multiplication. It's quite a result! It can be easily replicated for systems of equations with 3 equations and 3 unknowns.

[@JubeiKibagamiFez]

@@Faroshkas Just for reference, this is the first time I learning anything like this. I've never heard of Cramer's Rule or Matrix Multiplication before.

[@Faroshkas]

@@JubeiKibagamiFez That is nice. That means you can still learn a lot, and is already doing so!

[@VengerVideoGamer]

I remember using Gaussian elimination when I was doing Numerical Analysis in my maths degree about 30 years ago. I've never come across Cramer's Rule though and I would've done it the 3rd way that you showcased.

[@CalculusIsFun1]

Jordan-Gaussian and Gaussian Elimination(reduced Row echelon form and row echelon form). I like those because it looks satisfying.

[@tfg601]

Def easier to use this when doing a linear 3 systems of equations

[@TrimutiusToo]

I remember doing the elimination method but in matrices on my first year in uni during linear algebra...

[@kevv.1912]

I love the graphical method although any method is great and usable except graph one since it takes time to build a graph, I've been always taught to use elimination although whichever can be done fast is best. Graph is like really fun cuz it tells about about this relationship of slope y = mx+c and futher helps me to understand why f(x) is equal to y

[@F3IERABEND]

This is so much fun. Wish i had this much fun in school with math.

[@mcmable1]

Love brushing up on my math

[@sohailansari07289]

In the first method(an alternate way), you can first put x=0 and then y=0 and find the corresponding y and x-intercepts and then connect the dots to draw the line. Also you can use Cramer's rule similarly to solve a 3 by 3 system of equations ^_^ (Variables x,y&z).

[@stormswindy3013]

i like to just take the inverse of the coefficient matrix if it exists and it's reasonable, otherwise i just row reduce or use cramer's rule

[@starlightxfury]

hey bprp, what's the size of the whiteboard you use in these videos?

[@samueladler9080]

Making y the subject of both equation and equating the results just work as fine too, but I hardly see it demonstrated. From eqt 1, we have -(6-2x)/3=y, and from eqt 2 we 5-4x=y. Equate the two new equation since needles to say, y=y.

[@2012Ente]

Still remember starting uni and having to do the gaußian algorithm for solving these 3 by 3 systems😮

[@CeRz]

With the gaussian algorithm you can easily solve 10x10 systems. Make sure to have enough paper! 😂

[@2012Ente]

@@CeRz luckily 4×4 was the most we did, it wasn't fun let's put it like that

[@CeRz]

@@2012Ente I think we did 6x6 coefficient matrices on the exam at most. It was more about reaching echelon form and making conclusions regarding the amount of solutions, if any solutions, that matrix could possibly have. The people who didn't do their homework reached row reduced echelon form completely in vain!

[@ibraheem_Zain]

Where's the solution using matrices i was waiting for it 😭😭😭 but i loved the video anyway 😢❤❤❤

[@kevinstreeter6943]

It is the same thing with the coefficients put into a matrix. He wanted to explain the methods without introducing matrix.

[@muthiah9705]

Good morning

[@MathNerd1729]

Good morning! :)

[@malekabbr]

I know how to solve it in 6 ways! 1.cramers rules 2.elimination 3.substitution 4.graphinh 5.equilization 6.gassian(idk how to write his name) elimination

[@williamBryan-k2e]

Gaussian Elimination - well I saw what was a parital Gaussian Elimination - enough to make solving equation easier - as it does the elimination for you. so that after Gaussian Elimination - it is simple substituion. I say partial Gaussian Elimination - as when I saw it - it was for matrix solutions and I think it was more complicated than what I saw. - but here is Gaussian Elimination for solving equeations - and as I see it - it is for the elimination method - which I did without Gaussian Eliminiation - I would just look to how you could eliminate variables - by trying steps to elimnate - this is just another way to do the same thing.- kzbin.info/www/bejne/aJuYepZoi5yqp5Y&ab_channel=patrickJMT

[@champx5]

its gaussian

[@malekabbr]

@@champx5 thank you

[@AzureKyle]

I used the substitution method to solve it.

[@eclipseninja08]

So, Cramer’s rule is basically the method of cross multiplication when solving a system of linear equation in two variables

[@loganjones75]

Cramer's rule is even more attractive if you know dodgson condensation

[@JRSiebz]

"Dodgson, we've got Dodgson here!"

[@Sg190th]

I like substitution best.

[@EmmanuelGiouvanopoulos]

I ALWAYS SPOKE ABOUT CRAMER SUPERIORITY!!!!!!!!!!!!! LETS GOO

[@britishYES]

Crammer is a method of matrix isn't it?

[@junteo6712]

Gaussian jordan and inverse matrix

[@PoppySuzumi1223]

You won't know what is Cramer's rule if *Matrix* has not been taught before.

[@ericksakemi]

Be my math teacher pls lol 😂❤

[@faiqhussain9412]

Actually we learnt cramer rule but it was through the use of matrix.

[@SuryaBudimansyah]

Too comfortable in elimination method

[@epicstar86]

real

[@AllanPoeLover]

最後一種方法好怕記錯乘錯

[@williamBryan-k2e]

Crammers rule is a method - turing the equations into a matrix and then solving. Instead of just doing the match using the multipliers ( 2,3,6 ) and ( 4,1,5 ), it would make more sense if you drew the matrix and showed the math from there. I had forgotten this method just after being shown ( just threw it away I guess - because after looking it up, the memory kinda came back ). so look it up - en.wikipedia.org/wiki/Cramer%27s_rule - I think doing the other two methods is easier to rmember - as you have to remember how to setup the matrix's correctly to get the correct answer ( my opinion ).

[@williamBryan-k2e]

either of first 2 is the way that I would have handled it. as it is the method that had I had to use through most of my schooling.

[@SuryaBudimansyah]

Maybe he knows a different Cramer

[@williamBryan-k2e]

@@SuryaBudimansyah Not sure if joke or a real comment. so - I got the rule that he used - you can lookup url to see it. He just did the math without writing the Matrix's. what I said that if he had, it would make more sense. and I put in url so that someone could see it and say - ahh - now I know. If I misinterpreted and you were making a joke, my appologies.

[@savitatawade2403]

​@@williamBryan-k2e in my country, matrices are not taught until you learn calculus so, cramer's rule is taught to us just like bprp did