Solving Systems of Two Equations and Two Unknowns: Graphing, Substitution, and Elimination

We know how to solve algebraic equations, but what about systems that contain two equations? Is there a solution that satisfies both equations? There might be! Let's go over a few different strategies to find this solution.
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[@PhoenxFire]

We had a teacher with a doctorate in mathematics. I wish she could have explained this so easily to us. Sometimes having a doctorate does not make one a good teacher. Thanks for making this easier to understand!

[@Carrymejane]

Actually they help u to solve the equation but not to help their student know how to understand the method 'concepts' well, they fail to understand each student. What you do now is just summarize from ur knowledge u got from ur teacher in school

[@pianoboyedm4829]

thank you so much, my professor goes way too fast and never directly answers our questions, this helped our class out ALOT

[@PhoenxFire]

I hate when that happens!

[@adityadhardwivedi634]

hello professor, when you're going to explain and start tutorials of calculus? Actually I am very much excited for your super easy tutorials. Thanks for your efforts.😃😊

[@ProfessorDaveExplains]

don't worry they are coming soon! i have to get through geometry, more algebra, and trigonometry first, but within the year i'll get to calculus as well.

[@CartoonKidOLLY]

YAY it feels so good to understand the concepts and then get the problems right! I love you david!

[@scout0528]

Bro you just saved me for my algebra quiz THANK YOU

[@nicorobbins7589]

This boy in algebra two now lmao

[@BimkBomkCinematix]

lol @@nicorobbins7589

[@avenger5339]

how can some one be so serious yet so lovable

[@Concon-bu4bp]

Thanks dude. really enjoyed the manipulation followed by elimination, very cleaver way to approach the problem

[@Carrymejane]

At school I was never able to understand the algebra method 'concepts' well, and I only realized it now. Because at school we only focus on solving equations. We don't understand in focus and detail the method 'concept' for doing this. We don't understand it in its entirety so we just 'know' that to solve the equation it is only necessary to just 'follow' what's teacher did. Actually teacher doesn't do something wrong they great at teaching but they fail to know whether each student automatically understands a method in detail

[@reemyziz]

With checking comprehension, some y values don’t share a LSM. Can we multiple just one equation by a number so it matches the other?

[@Regular_Decorated_Emergency]

Thanks so much! I finally understand what to do if you can’t subtract y from y to get 0!

[@SSP600]

THANK YOU SO MUCH

[@_vineet7865]

Thanks for explaining this ❤️🔥

[@is6815]

Does this work on any function? Ex. Trig,Polynomial etc.

[@lexielea873]

Holy shit you just taught me something that actually made sense for once and I’m so happy thank you

[@maddyeldy2487]

Thanks prof. Dave 👌

[@MB-st6id]

Amazing video

[@Xboxlove1]

well done

[@Mecha_Math]

So good

[@noemiflores5076]

Hi professor Can you explain how to do Proportional and Non Proportianl? Thanks

[@NickHope]

I hope Penelope got paid overtime.

[@Regular_Decorated_Emergency]

LOL.

[@ridmicmeena4123]

Can u give the solution of comprehension i keep getting it wrong

[@vernie7882]

Can you explain where you got: if A = B and C = D then A + C = B + D and that it proves that it applies to the equation above? It makes sense by itself but how do I know if the two equations are in any way related to that logic and how it helps us in solving them?

[@zerglin9000]

For his example, A is the value of the first equation on the left of the equal sign and B is the value on the right. C is the value of the first equation on the left of the equal sign and D is the value on the right. so his two equations would be A = B C = D so if A=B and C=D, then A + C = B + D. This is relevant because we can use this information to do elimination, as we know that by adding or subtracting B on one side, we can add or subtract D on the other side to preserve the equality in our equations. it makes sense if you assign values to your variables. EX: when A is equal to 1, well A = B so 1 = B. This means when you are adding or subtracting one set of equations (A = B) to your other set of equations, you are preserving the original equality: eg not changing the values for your equations.

[@marcodaniel5446]

I don’t know what’s going wrong but different methods are giving me different answers pls send help

[@azizghalib495]

Thank you professor. But could you elaborate on how does the logic of A+C=B+D relates to system of equations. In other words, what variable corresponds to which term.

[@zerglin9000]

For his example, A is the value of the first equation on the left of the equal sign and B is the value on the right. C is the value of the first equation on the left of the equal sign and D is the value on the right. so his two equations would be A = B C = D so if A=B and C=D, then A + C = B + D. This is relevant because we can use this information to do elimination, as we know that by adding or subtracting B on one side, we can add or subtract D on the other side to preserve the equality in our equations.

[@anusriiii]

You made it so easy.. thanks a ton

[@captaingaz8705]

You need to make1 on comparison method

[@nteproductions1083]

Could’ve used a lot of this yesterday on the PSAT

[@Regular_Decorated_Emergency]

Well then better damn use it for the SAT!

[@OkSid300]

Certainly a very productive lesson! But it would be great to have more real life examples.

[@johnymnemonic4657]

There are more ways to solution.Cramer,s Rule and Gaussian ellimination.

[@mar-ww3if]

professor i ended up with x=11 and y=-5 for the last comprehension example , are they alternative answers ?

[@Teiwaz111]

6x + 6y = -24 3x - 3y = 48 Multiply the second equation by 2 6x + 6y = -24 6x - 6y = 96 Now add them up to get rid of y 12x + 0y = 72 Solve for x x = 72/12 x = 6 Now use that in the second equation to solve for y 3*6 - 3y = 48 18 - 3y = 48 -3y = 30 -y = 10 y = -10 There are no alternative answers, as there is no alternative medicine - it either is an answer or not, it's either medicine or not.

[@mar-ww3if]

@@Teiwaz111 you are kinda Late but thanks anyway

[@saniconeiljoshuac.2084]

What is the 2 equations are both positive?

[@RedMetalSuit]

How do you do elimination if the Y in both equations is negative?

[@kcf29jdf30]

maybe multiply negatively? idk

[@Jourvence777]

I've done it

[@anna.candrink7251]

You explained this like it's so easy💞 Now, I feel dumb for not knowing how to solve these equations before🤡

[@kevinjohn1789]

Legend

[@Breadin]

Please help I can't understand

[@fazulrahmanhamidi8895]

Why write two equations to solve two unknowns? What is the reason?

[@ProfessorDaveExplains]

It is impossible with only one.

[@ta_ogboy9998]

A solution to one equation won't mean it will be a solution to the other equation. You want to find a solution for both equations.

[@Carrymejane]

It's just a reference to learn, like how a question make in the exam from the central

[@xeqqail3546]

For the 5x + 2y = -18 x - 7y = -11 isn't the answer is x = -4 y = -1 ??

[@trundlegaming8019]

no its not, its just 1. Beacuse when you have 37y=37, its y=37/37 it dosent change to -37

[@Ethiopianexposer]

Jesus Christ, that was easy

[@kimzlife5993]

You explain too fast