Art of Problem Solving: Systems of Linear Equations with Three Variables

[@meow9426]

This is so helpful. Next time I go to the grocery store to buy shit ill use linear systems with 3 variables to figure out if my tomato soup is boneless

[@nonutkyle5363]

LMAOO

[@ran-vc4wt]

i saw in that one video-

[@roxannamendoza3402]

This is so much easier than the way my teacher taught it to me. I would take 20 minutes or so to just answer one question. Organizing the equations with letters makes it better to understand. Thank you for the help!

[@liz12276]

YOU ROCK. I’m a tutor, I needed a refresher, your method did the trick!

[@TheNamesWolf]

I love how you tried to combine art with math. Its like combining war and peace.

[@anaklusmosgreek3198]

You are like Steve from blue's clues and i appreciate for you breaking it down for me

[@Zayistan]

I thought that was Nicholas cage

[@prafulsakore5752]

Zaynab Ahmad I also feel same thing😂

[@megamandiNL]

I laughed way too hard at this.

[@alexwang982]

He’s richard

[@salmanrajon4808]

😂😂

[@hilal1433]

Really carbon copy

[@TOILETSMELLER13]

Yeah I'm still so confused.

[@DeBellanadi]

haha me too , it makes sense but the fact that it can go more than one way , its confusing !

[@mojicaw2]

let's accept the fact that, we all have to go through this problem or else ..

[@abdulhalim520]

Guys, don't be despondent. This problem has many methods to solve, but the two I use are used in calculus and are very effective. .Firstly, find the equation in A and B, which produces D, if you like. .Then find the equation in A and C, which produces E. .Then find the solution to one of the variables using D and E. .Use solution gained from D and E and substitute it in either D or E, which will give you the solution to the second variable. Now, that you have found the two variables, the rest is easy. .Substitute them into the original equation(A or B), which will produce the solution for the last variable.

[@snshusat161]

hard to believe that anybody can be confused over this simple method.

[@bkcovers1184]

Shub it’s not simple to me

[@declanpeters3305]

Love this video! You explain it much more simply than my math teacher.

[@baddiebell3]

you are my actual saviour, love you man

[@SenseOffenseStudios]

Math by Nic Cage

[@Ray-fi4oc]

My thoughts exactly: made it so much more entertaining!

[@kdj94]

This is actually my first time commenting on a KZbin video Thank you very much for explaining

[@xyomaramendezhernandez4676]

How do you know which number to multiply each equation at the beginning?

[@shaun7096]

Xyomara Mendez Hernandez I know it’s probably too late now but you multiply it by whatever number will help you get rid of a variable

[@shariqueahmed8111]

i love your energy in this long boring solution, as u said its a tip of the iceberg

[@michaelriad4272]

Great Work, you're enthusiasm matched with the simplicity of you're explanations helped me understand it with ease. Thank you so much :)

[@Bilbus7]

YES! this video was perfect. So easy to follow!

[@sammylee1895]

How do you now which equations to sub in X, Y, and Z after you found one of the variables?

[@constantineq643]

You could use any of the equations for substituting tha variables, he just chose the one that looked easiest and went with it.

[@kennethcramm6115]

A great video that shows students how to keep track of the information inside these types of questions. That skill must be mastered to confidently solve systems. I request you add the ordered pair solution of (x, y, z) as the final form; a point in space.

[@marioansong3675]

can you substitute numbers you get at the beginning into any other equation to find x or y?

[@Chubimaster343]

Thanks so much, 'twas excellent. Now I'm gonna watch it again to make sure I'm good on the subject

[@fijit4]

are there any rules about which equation is added or subtracted from which? like, do you have to add or subtract all equations from the same first one? a-b and a-c?

[@creampuff966]

You can use any combination of equations and you'll still get the same answer. You can use a-c and a-b, or b-c and a-b. Whatever works for you :)

[@panndorasbox]

what kind of screen or tv or aftereffect you using to wright on screen?

[@mr.snoopyscoops28]

A smart board I guess in my school teachers use it to teach and sometimes use the black borad

[@TomDensley]

Best video on the subject! Thanks

[@shababanjum1129]

Whats that thing u r using to write?

[@willbegood2012]

very nice illustration. Thanks a lot...

[@gunsmoke5580]

So helpful... Teacher went over this shit way too fast. Could understand anything she said.

[@MarshmallowLovesDano]

omg HAHAHAHAHAHHAAHA that was my exact reaction when i first saw that freaking question...

[@creampuff966]

lol saaaaaaammme

[@animeshbarve8564]

👍👍 thank you sir your way of explanation is great

[@majorjnr1880]

you are the great lecture cause you made me think like we are leaning together .thumbs up

[@qiarramartinmyers3355]

EXTREMELY helpful. Thank you !

[@basic_Handle]

I like ur board & I like ur way of teaching.

[@eu_lyr1cal407]

thank you so much this helped me immensely with my year 9 home work

[@donaldbiden7927]

Atleast there are 3 equations and 3 variables... we have 1 equation and 2 variables in number theory (along with another constraint like all solutions are integers)

[@stedis7259]

What an amazing teacher

[@billychelagat3835]

Thanks Richard...May God bless you.

[@sarwaranwar3485]

what if coefficients of variables are also in the form of a b and c like a1x+b1y+c1z ,a2x+3b2y+3c2z and a3x+b3x+c3x

[@jonahwright]

how are you writing on the board?i wanna do it too

[@SamuelKioEDH]

giant ipad

[@kgonzalez5458]

first time seeing your video but it's great helped a lot and couldn't help think that I'm watching blues clues for math

[@soheibdissa9991]

This helped a lot!

[@jacobsanchez1587]

Can I just row echelon it?

[@magick2006]

WOULD B and C work as well instead of A and C?

[@erljencalinawan9706]

What about if it's nonlinear?

[@armeniancinematiclegacy994]

Great teacher and actor!!!

[@thecuteangel777]

Thank you so much! I appreciate your help!!

[@wesleynation8597]

why did you multiply equation E by -3?

[@appleheadjackson3524]

Wesley Nation He was canceling out his x's to find his z's

[@castiron1973]

Great! Thanks, very easy to follow!

[@hazimhidayat8886]

this guy solves better than what my textbook show

[@katherinehuynh2134]

Can u become my new math teacher 😁😁😁😁 video explained everything thxxxx

[@jomarbonje3496]

Great sir! Now I understand thanks.

[@chiragm9695]

Thank you ,it was simple and amazing 🔥🔥

[@narushio3]

how do you know if a system of linear equation has no solutions, infinite solutions, or one solutions?

[@manuelvaltierra2105]

This helps a lot

[@Golaoromoo3]

Thank you! Tomorrow I have exam

[@darwindelaisla5343]

I don't know. But how is it -z? 5z+-6z= -z in terms of -1z?

[@sagnikdey2465]

Awesome video. But also, are you familiar with someone by the name Nicholas Cage?

[@alstroemerimations6328]

Sagnik Dey I'm not the only one!!! XD

[@shahibnulsadekwafi6367]

What if u only have 2 equations, can u derive a third one?

[@dewanshsingh2384]

really helpful, thanks

[@slewis9647]

omg thank you so much. Bless your heart for making this video!

[@HexFire03lmao]

0:10 new meme format

[@justintime89]

Thank you!! Crystal clear!

[@PanookyDooky]

what about if I have to find "m" . Like the system: 2x+y+z=0 , x-y+mz=o, 3x+y+3xz=0 ?

[@mr.danielolivobapctcna8322]

You're terrific. It was entertaining.

[@Sauce-ke]

instead of using letters like D,E,F,G, I suggest you to use A1,B1,C1 instead. A lot more letters is more confusing

[@kimcharlenetyne1982]

is it just me or does your plug in for B not calculate i get - 5(3)-2(7)+4(-8) = -31 not 25?? But A & C work out ok (confused!!)

[@jassxoxo1317]

I DONT GET IT

[@bdeshiguy]

JasS Xoxo I can help u

[@varenyagupta3012]

@@bdeshiguy you are an year late

[@alexwang982]

Lol

[@huai805]

Thanks a lot

[@KhrystaPlays]

Loved it!

[@xEpTICSHOTZz]

Thank you so much!

[@diorrat..0]

Swag

[@sergiogutierrez9878]

Very Helpful :)

[@janetteharris3477]

Best out there!!Awesome!! Thank you!!

[@mmoproductions6217]

this dude looks nothing like nicholas cage...

[@naraechunsa]

thank you !!

[@garrettsmiley4408]

I like you. You are getting a new subscriber.

[@kahalamathvidz]

thank you so much man

[@the_Cinema_Talks]

Thank u so much sir .

[@alstroemerimations6328]

not gonna lie the thumbnail makes him look like Nicholas Cage teaching math XD

[@JohnEveryMann]

why do we multiply equation b by 2??? i dont understand.. If someone could explain that to me i would be very grateful

[@Animatorskeleton]

Because see the 4y in equation A ? You need to cancel that out, in order to do that you need a -4y. You get that by multiplying equation B by 2, hence the -2y in equation B becomes -4y, then when you add the two equations together, the y values cancel out, making the equation solvable :)

[@antoniovega1800]

Elimination

[@yasminbedrosyan8987]

great way

[@danielkosznirczuk9703]

Hello, Can someone please help me with this equation?? I always get lost in the way... e + fn + g = 9 2e + fn + g = 20 9e + fn + g = 37 I can't do it :(

[@diorrat..0]

I think- (I’m not sure) (9e + fn + g) - (2e + fn + g) = 37 - 20 (9e - 2e) + (fn - fn) + (g - g) = 17 7e = 17 e = 17/7 Substitute e. 17/7 + fn + g = 9 Multiply 7 on both sides 17 + fn + g = 63 fn + g = 63 - 7 = 56 g = 56 - fn Substitute again into any equation you like. Check your work

[@diorrat..0]

Just realized it was 3 years ago lol

[@hashimalsebaie4939]

Thanks

[@adeelsadruddin3402]

how to solve if we have zero z lets say?

[@marysaotomeuwu]

What's the answer for x + y=6 y + z=-5 z + x=7 with steps

[@mrmusicstore]

+AsianBobFriend idk if you still need help, but....here you go, try the question by following these steps side by side other wise this will be useless even if you understand it :) STEP ONE: Eliminate Z from equation (2) and (3) just like how the video showed. -Y - Z = 5 [Equation (2) times -1] X + Z = 7 [Equation (3)] (+) _________ -Y + X = 12 [Call this equation (4)] (Hint: it's like you are combining equation (2) and (3), to have only 1 equation) STEP TWO: Now Use elimination on equation (1) and equation (4). STEP THREE: Then you should get the value of one of the unkowns, either X or Y depending on which unkown you eliminated. STEP FOUR: Then find the other unkown by putting your unkown that you just found into equation (1) or equation (4) either way works. You should get x=9 and y= -3. STEP FIVE: From there since you know X and Y just find Z from equation (2) or (3), any of those two equation will do. Z = -2. X= 9 Y= -3 Z= -2 Your Welcome, peace.

[@NabeelAhmed-ln3fw]

x+y=6 so y= 6-x put value of y in 2nd 6-x+z=-5 -x+z=-5-6 -x+z=-11 z=-11+x now put the value of z in 3rd -11+x+x=7 +x+x=7+11 2x=18 x=18/2 x=9 now put value of x in 1st 9+y=6 y=6-9 y=-3 now put value of y in 2nd -3+z=-5 z=-5+3 z=-2 so x=9; y=-3 ; z=-2 now put values in any equation to verify.

[@NabeelAhmed-ln3fw]

x+y=6 so y= 6-x put value of y in 2nd 6-x+z=-5 -x+z=-5-6 -x+z=-11 z=-11+x now put the value of z in 3rd -11+x+x=7 +x+x=7+11 2x=18 x=18/2 x=9 now put value of x in 1st 9+y=6 y=6-9 y=-3 now put value of y in 2nd -3+z=-5 z=-5+3 z=-2 so x=9; y=-3 ; z=-2 now put values in any equation to verify.

[@elifetuba4773]

how are you solve it?

[@elifetuba4773]

how are you solve it?

[@akdr12345]

isn't negative 12 plus 5 a negative 7?

[@_alphasierra4705]

Dara Ryan try actually pointing out where that step is if you are looking for help

[@_alphasierra4705]

Dara Ryan oh...so you mean the checking part: Here, near the final step, you have -y-5=-12 If you add 5 to cancel out the 5 and add 5 to the other side, you will have -y=-7 In this case, you just want to remember, you do not want a negative variable in your answer, ever, it can still be simplified. You see, there is still that imaginary negative one in front of the y so to get rid of it, you divide by -1 on both sides and -7 divided by -1 is 7 Negative/negative=positive

[@viktorsapundziovski6751]

Thank yoooou soo much!!

[@Mangalsirguidance]

Thanks sir

[@farheenislam568]

Thank you so much ^_^

[@squishymochi9627]

Whose doing this in Kumon , and came here because they are too bothered to read the example

[@MuhammadTalha]

thnx a lot

[@actigraf23]

Really helpful ! Tip: Do it with him

[@skp8933]

good video sir

[@warnerrasmussen6921]

It did not help when you added more equation labels; there are only 3 equations in question and that completely threw me off...

[@M_Chen333]

3 is my favorite number.

[@reborn5448]

x+3y+3z = -1 2x-y+z =-3 3x+5y+7z=-1 Can you solve this?

[@stephenbarker8325]

hi solutions are X = minus 4 Y = minus 2 Z = 3

[@AwesomeNX]

Thanx dude

[@eu_lyr1cal407]

you are the best

[@wenvyagam1142]

shouldnt it be -50? instead of +50? because its on the other side of the equal sign...?

[@evelynpasco4785]

im kstill on confusion

[@sspurgatoryx8773]

This was a nightmare in Algebra 2

[@noorashams5027]

I loovveee this

[@EddieRuiz-l5c]

good!!

[@mosialive]

Just use Matrices. . . I used to teach students the same method. They get confused. . . They found matrices way easier

[@clashbrosbraul174]

+Mosia Thabo Most Adept Its best to know both