Systems of three variables | Systems of equations and inequalities | Algebra II | Khan Academy

Systems of Three Variables

Missed the previous lesson?

Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Algebra II channel:

[northernillinoishunting]

thank you so much, too study for all my tests I just go through the problems and find one of your videos for the problem type I'm on. You make so many people's lives easier. I can never really understand my teachers too well but when I watch your videos it just clicks. Once again thank you!

[Nutty]

You make it look so easy. I keep getting wrong answer even though i'm following all the steps.

[tania_rtga]

Can you in the future use bigger numbers instead of just 1y bc that's easy

[jennidarqnys]

Thank you. I love listening to your upbeat voice.. makes it less frantic for my brain.

[marhb]

omg he made it soo easy when my teacher took  a whole week just to teach us this and I didn't understand a thing till  I watched the video

[julianeluna]

I spent 2 hours trying to put a 3 variable system in row echelon form. After I watched this video, I went back to that problem and it took me 5 minutes. Thank you so much.

[jimmy_dz_nutz]

Is this done by the process of elimination or substitution?

[bankaikun]

I'm confused as to why the equations would be added. For instance, on an XY plane, the solution for the point of intersection between two linear equations is solved when the equation are equal to each other.

[arianaarnold]

THANK YOU, I'VE BEEN TRYING TO DO THIS FOREVER!!! Very effective explaining with nice color coding to make it super easy! All the math teachers should try to teach like :)

[_wrld_peace]

i cant understand my professor when he explains this in class. He uses the addition method. he confuses me.
im going to practice on this problem. i hope i get it. i need to underatand it.
thank you!

[brandenish]

Thank you for the video. I got a question. How to we solve systems of three that variables come to different numbers in each system? Am I solving it wrong or do they suppose to be like that?
I. x-6y+z=1
II. -x+2y-4z=3
III. 7x-10y+3z=25

[Jonnemanne]

I love it when Sal's voice RISES when he EMPHAsizes something. :) We need that in Finnish education.

[sagool]

It's amazing how you teach it so well compared to some teachers who skip steps and assume everyone understands.

[camed]

in general can a variable like "z" be a fraction?

[BTNHarmony]

In the second step at 4:03 you say" 2z minus z" but throughout that operation you are adding. Obviously the answer is the same but wouldn't you say that you are adding 2z to a negative z. I was under the impression that you have to subtract the entire second equation for the first or add the entire second equation to the first, which ever helps you isolate the variable. Subtracting one portion and adding another seems inconsistent and confusing.

[copiludeargint]

How to let s say construct a system of 3 equations with 3 unknowns that have only 1 solution?

[mlgcoxie]

Thankyou so much! I’m a uni student and I learnt this in Highschool but I forgot how to do it. Uni doesn’t give you much help so thank you for the very well explained reminder!

[eddielloyd]

How about:

6 = a + b + c + d

14 = a^2 + b^2 + c^2 + d^2

36 = a^3 + b^3 + c^3 + d^3

[FireStrikeKiki]

This heped so much! I understand it now :D

[IbrahimAbdAllatif]

what if there was a bigger than or equal comparator instead of the equal comparator in each equation how could it be solved in that case ?