Consistent Independent, Dependent and Inconsistent

Learn about whether a system of linear equations is consistent independent, consistent dependent or inconsistent in this free math video tutorial by Mario's Math Tutoring. We go through a couple different ways to solve these three examples.
0:16 Three Things that Can Occur with 2 Lines in a Plane
0:45 Definition of Inconsistent with Diagram
0:57 Definition of Consistent Independent and Consistent Dependent with Diagrams
1:27 Example 1 Rewriting the Equations into Slope Intercept Form
2:09 Second Method of Solving Using Substitution
2:39 Example 2 Rewriting the Equations into Slope Intercept Form
3:16 Substitution Method and How to Identify that it Is Consistent Dependent
4:07 Example 3 Showing Consistent Independent
4:46 Using Substitution Method to Show Consistent Independent
Related Videos:
Substitution Method
• Substitution Method fo...
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- Mario

[@milanatarasova5588]

Mario's Math Tutoring thank you!

[@sultanmahmud7029]

Thank you i understood and enjoyed the video very much.

[@MariosMathTutoring]

You’re welcome Mahmud!

[@finlaybaines3312]

Thanks, I am just cramming before a test next block and this helped sooooo much

[@MariosMathTutoring]

Glad my video helped you Finlay!

[@smirkykiller9486]

@@gabbygabs8271 The guy that commented is Finlay

[@benthebloon9588]

I love how this guy responded to every comment on this vid it’s so sweet 😊

[@oat6984]

BESIDES YOURS LMAOOOOOO

[@smirk4554]

@@oat6984HAHAHAH WAS GONNA COMMENT THE SAME

[@eehub6710]

You are a great teacher ❤️, you explained the concepts so beautifully ,keep making more videos,may God bless you with lots of happiness 😊🙏

[@MariosMathTutoring]

Thank you for your kind words. Glad my videos are helping you.

[@RagedN1]

Thank you so much for this video, I understood this better than my own math teacher. Maybe because I wasn't paying attention in class.

[@jesteramogus2186]

Lol same

[@yaweli2968]

Omg you are too good. This is even no brainer with geometric interpretation. It’s so so complex with Professors who can’t teach.

[@MariosMathTutoring]

Glad you liked the way I presented this video Yaw Eli!

[@meapetals]

made 7 years ago, but still very beneficial. Thank you so much, better lesson than aleks!!

[@camaluck678]

Studying for my end of year final, 20% of my overall grade. Thanks!

[@MariosMathTutoring]

You’re welcome! Good luck on your final!

[@camaluck678]

Mario's Math Tutoring Thank you.

[@providence3977]

How did you do?

[@camaluck678]

It was quite a while ago so I don't remember the exact grade, but I believe I got a B.

[@providence3977]

@@camaluck678 Nice! :)

[@salemisjuucy]

dude, you explained this way better than my teacher lmao, thanks.

[@jingjabanes9736]

Bruhh. I Just Skipped 19 Math Modules. because I dont Understand the Topic. But When i Saw This Vid. My Brain Instantly Fixed Itself. Ur A Good Teacher TBH.

[@ops_sah105]

I’m late , but this helped me so much. Thank you

[@bibeksssyadav1014]

Thank you sir

[@MariosMathTutoring]

Your welcome!

[@tymccauley8653]

Wonderful video very helpful for my intermediate algebra college class thank you sir

[@ytclippedshawnn1088]

Learned in less than 3 minutes ty

[@Navek1977]

Thank you so much for this. Well-spoken, a great display of the explanation on the board, and straight to the point.

[@bhargavrailguru1818]

thank u sir for the explanation from india
bengaluru

[@MariosMathTutoring]

You're most welcome!

[@rajeshwari152]

Super sir...I really understood😍it in easy way

[@anwari03]

Thank you Dr.

[@andreavincent4619]

Wow!! Thank you so much!!!. You explained it very well.

[@MariosMathTutoring]

Glad you liked the video Andrea!

[@brandencolie1356]

beautiful explanation :)

[@krishnamarichetty101]

I have a placement exam coming up, so thanks for your help

[@MariosMathTutoring]

You’re welcome Krishna! Good luck on your placement exam!

[@mm61777]

Thank you so much! You explained everything perfectly! Thank u!!!

[@Manichandan022]

Thanks for helping ❤️

[@aadityamaharaj4082]

Love it Sir

[@theblarneystone1023]

this video really did explain the concept clearly. Thank you.

[@yousefisahuman8610]

THANK YOU I AM SAVED!!!

[@warriorskitcat3859]

WOOOPERR

[@xeiisbusy]

2:00 but i thoughr you were suppose to multiply not add it? That's what my teacher thought us and im confused

[@steph3470]

I understand you better than my math teacher lmaoo thanks, mister

[@MariosMathTutoring]

Glad my videos are helping you Camzi!

[@crazygur1y]

I appreciate this video

[@user-kn8xj8td2k]

Thanks so much!!

[@MariosMathTutoring]

You're welcome!

[@manishadwivedi4005]

Thanku soo much sir for such nice explanation..

[@leatampis2908]

Omay gash this video help me thank you so much

[@prabeshbhattarai4210]

Thanks man
Good job

[@MariosMathTutoring]

Glad it helped

[@henry6871]

Very clear and concise explanation. Thank you, sir

[@MariosMathTutoring]

You’re welcome Esteban! Glad you liked the video!

[@angelobello3892]

Thank you sor

[@shasiyashasiya9605]

very very very ..nice ,,,,,,,,,,,good video///

[@MariosMathTutoring]

Thanks Shasiya!

[@whitneycarpenter691]

Very helpful! Thank you!

[@colagirl1793]

I literally can't thank you enough

[@satim-fiream9146]

WOW THIS IS EASY YOU MADE IS SO MUCH EASY!!!!!!!!!! MY TEACHER WAS SO CONFUSING AND DRAWING LINES EVERYWHERE AND I WAS LIKE "WHATS GOING ON" BUT NNOW I GET IT!!!!! THANK YOU SO MUCH!!!!! MATH IS FUN IF YOU MAKE IT EASY HAHAHHA THATS WHAT MY TEAACHER BE SAYIN

[@MariosMathTutoring]

Glad my video helped you understand this concept more easily!

[@jaybeo9144]

Thank you this was very helpful🙏🙏🙏

[@MariosMathTutoring]

Glad my video helped you Jaybeo!

[@truetalk5753]

this is a good video

[@MariosMathTutoring]

Thanks True Talk!

[@TheHiroClaw123]

I wonder why they named them as such?
I like to think of it this way:
Say we have two equations that are literally the same equation Maybe they're rearranged, maybe not. And they are two lines of a system. AKA on a graph, these two lines intersect infinitely because they are the same line.
Thus, their EXISTENCE is DEPENDENT. Because one line exists due to the other.
However, when we have parallel lines or 2 lines that intersect once, we have two SEPARATE lines that EXIST separately and are considered as such. So, we can call them two INDEPENDENT lines.
These independent lines can either intersect once or not at all. If they intersect all the time, they're basically the same line, and are no longer independent, therefore dependent.
If they intersect once, we can say they HAVE one solution. These two equations in this system HAS one solution. Hence, the system CONSISTS of a solution. Hence, CONSISTENT.
If they have no solutions, AKA parallel lines, they DO NOT CONSIST of a solution. Hence, INCONSISTENT.
math terminology is weird

[@firedropper]

this is such a good explanation dude thanks

[@i9xp]

OH MY GOOOOOOD THANK YOU SO MUCH

[@MariosMathTutoring]

You’re welcome!

[@iivector8994]

thank you so much

[@mizukiyamada2371]

Thanks it helped :D

[@JahanAcademy]

very nice

[@MariosMathTutoring]

Thanks!

[@Johnwilliams-th9hq]

You just explained in five minutes what my techers took 1:30 to do

[@MariosMathTutoring]

Glad my video helped you quickly understand this concept John!

[@ani8662]

amazing help! thanks

[@MariosMathTutoring]

You’re welcome Ani!

[@hqs9585]

What is it meant but independent and dependent??? in your examples

[@ivannolia5458]

thank you! very helpful 🙂

[@MariosMathTutoring]

You’re welcome Ivan!

[@burpie3258]

Thank you!

[@MariosMathTutoring]

You’re welcome burpie!

[@Joe_lawexy]

thank you.

[@MariosMathTutoring]

You’re welcome Joseph!

[@izumikyouka1645]

at 2:11 he said add -1 both sides so 5x plus -1 equals 5??

[@paulaberi2132]

Not sure if you ever got your doubt sorted out, but by that he meant to add 1 to the negative one on the left side of the equal sign and add one on the right, so that way you get rid of the negative one on the left (leaving you with 5x) and on the other side you get 13.

[@Weekendwitrahul]

I really dont know, why do we call them consistent or inconsistent aprat from their solution what the reallogic behind the us eof this word

[@plthaploo7629]

Sir i have a question that are intersecting lines and coincident lines both consistent??!!

[@isabellag9692]

much appreciated

[@MariosMathTutoring]

You’re welcome!

[@zachhenry9575]

Test tomorrow hope it goes well 😬

[@MariosMathTutoring]

Good luck on the test Zach!

[@lilyang5861]

Write a system of equations that are consistent and independent that passes through point ( 6, -11)

[@nirmaldeshprabhu4905]

U just made it crystal clear.. Thankz a ton😊✌️

[@MariosMathTutoring]

Glad my video helped clear things up Nirmal!

[@enithnaivy4280]

Would parallel lines be dependent or independent?

[@luislora2544]

i love it but it's soo fast HAHAHAHAH

[@SAGARTWR786]

I still don't get it why lines having one solution are independent and lines having many solution are dependent. Also if I am not wrong lines having no solution are independent. Could you please explain me with some example?

[@MariosMathTutoring]

Sagar, linear systems are either consistent meaning they have a solution (one point of intersection is referred to as consistent independent...infinite solutions (meaning the two lines are the same) is referred to as consistent dependent). Parallel lines have no common points of intersection and are referred to as inconsistent. Hope that helps you!

[@cr4nch.557]

Exam tomorrow and im not going to fail even im not very smart...

[@madamtirkulon3344]

Hi, can you help me to my math??

[@roxannedesjarlais8989]

how do you write the ordered pairs when they are dependent??

[@MariosMathTutoring]

Good question...when they are dependent it means that both equations represent the same line which means that every point on the line is a solution of the system...most of the time you can just say infinitely many solutions or you can say consistent dependent...hope that helps!

[@nishakaushik7899]

@@MariosMathTutoring Thank u so much sir .I was also having the same question.

[@MariosMathTutoring]

You’re welcome Nisha!

[@vikaspal2486]

Anyone from India

[@tunadody]

like and sub
thx man
.

[@joshualoydgacad7762]

Bruh ur great but slow down pls

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U are looking like jhony sins

[@shernaj255]

dependent and independent of what? well explained otherwise

[@NouhouBarry-qt8uy]

im not sorry

[@nelsonquilling4336]

I can't understand 😡

[@MariosMathTutoring]

Do you have a question about the video Nelson?

[@ashv2038]

So small,I can't understand

[@wayde2]

what

[@fishyfishyfishy500akabs8]

thank you

[@MariosMathTutoring]

Your welcome!