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

Art of Problem Solving's Richard Rusczyk solves a system of three equations with three variables.

[meow]

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

[roxannamendoza]

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!

[anaklusmosgreek]

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

[TheNamesWolf]

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

[MarshmallowLovesDano]

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

[belleobura]

you are my actual saviour, love you man

[liz]

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

[declanpeters]

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

[xyomaramendezhernandez]

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

[michaelriad]

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

[kennethcramm]

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.

[gunsmoke]

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

[Bilbus]

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

[sammylee]

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

[kdj]

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

[donaldbiden]

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)

[Chubimaster]

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

[shariqueahmed]

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

[fijit]

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?

[willbegood]

very nice illustration. Thanks a lot...