Solving Systems of Equations... Substitution Method (NancyPi)

MIT grad shows how to use the substitution method to solve a system of linear equations (aka. simultaneous equations). To skip ahead: 1) For a BASIC SUBSTITUTION example, skip to time 0:19. 2) For an example where it's TRICKIER to solve and also involves FRACTIONS, skip to 08:17. and P.S.) For WEIRDER-LOOKING DIFFERENT FORMS of systems, for which you can still use substitution, skip to 16:46. Nancy formerly of MathBFF explains the steps.
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For how to solve a system of linear equations with the ELIMINATION METHOD, jump to: • Solving Systems of Equ...
What does it mean to solve a system of equations using the SUBSTITUTION METHOD? It means to solve for the x and y values that make both equations true, using the substitution method. Substitution is just one way of solving (elimination is another way). Here are the THREE STEPS you can always follow:
STEP 1) First, solve for x or y in either of the two equations in the system (get x or y alone on one side). It doesn't matter which equation you use first, and it doesn't matter whether you get x alone first or y alone first. You can pick whatever looks easiest to solve for in the system.
STEP 2) Then, take the expression you found for y (or x) and plug it into the other equation you haven't used yet. For instance, if you got y alone in the first step, take that expression for y and plug it into, or substitute it into, the variable y in the other original equation in the system. Then, simplify the expression by distributing to open up the parentheses (using the distributive property) and combining like terms. Solve for the unknown variable in this equation.
STEP 3) Finally, once you solve and get an actual number for a variable, you can take that number and plug it back into either original equation in the system and then simplify and solve for the other variable. This (x,y) pair is your solution.
IMPORTANT: If you get something like 0 = 0 or 8 = 8, or something like 1 = 2 or 0 = 21 when you are following these steps and trying to solve, then you've probably found a special case. If you get something TRUE like 0 = 0 (a number equals the same number), then there are an infinite number of solutions to the system, and you can just write "infinitely-many solutions". If instead you get something FALSE like 0 = 21, then there is no solution (inconsistent system), and you can write "no solution".
For more of my math videos, check out: nancypi.com

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True

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It’s because she’s hot and your paying attention and your most likely.

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Math: exists My brain: *explosion*

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It’s honestly not hard it’s you making yourself think it impossible and it pretty difficult but once you practice and get the concept down it pretty easy.

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Bro maths is not that hard. You need to learn all those formulas and understand the concept

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Omg riiiight never on practice you take a test and then bam it's there like wth. Why didn't they show this to me in practice. 🙄

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So truee

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lmao this is so true. Literally just had that happen to me on a test

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🤨

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I literally had a panic attack because I have a test tomorrow on this and I just thought that I was dumb for not understanding what my teacher was saying but now I know that its his fault for teaching it in a bad way. the way you teach is very calming and reassuring and that helped me understand this super well so thank you so much

[@victoriamorin9770]

lmao same tho. I do online so i only have the lesson to try and learn from and if i need help i have to set up a call with my teacher so it makes it harder to get help

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Recognized how hard it is to write backwards......

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Shes not writing backwards, she's just flipping the video so to us it looks like shes writing with left hand, but shes actually writing with her right hand

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@@a-level88 ^ lol

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Agreed, but what if she is also right hand dominant? Even more impressive.

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Oh yeah yeah

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she might be using a mirror which would flip the whole image

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im not even paying attention im just amazed on how she can write pretty backwards and also trying to figure out what shes writing on maybe on glass? thin air? idk

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editing....

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I assume it a piece of glass and a mirror.

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[@lenliz2003]

so true

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its quite confusing how she does it

[@Regular_Decorated_Emergency]

Nancy is my favorite math tutor on YT! 😭😭😭😭 Thank you so much! You are even better than Brian McLogan!

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The COrona virus is upon us and I'm watching this video, it was really helpful! thanks!

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Are you in class 10th tell me😊

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Ya I agree because I am in grade 7 and I still struggle

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im in 10th grade :p

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Still not done

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Still not done from future

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"You don't have to like math but you can like my video" I don't like math but I have liked every NancyPi video I've ever watched because you're always so helpful! I like how you somehow manage to squeeze entire lessons into 20 minute videos without losing me at any point (which is what usually happens with other YT instructors). Thank you and keep making more videos ❤

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You have, in a single video, shared your knowledge, clearly and with great patience, for the betterment of my incredibly frustrated and challenged mind! I am forever grateful for your talent and thoughtfulness; please keep making videos ( algebra specifically). I “get-it” now, thank you!

[@Msttobe]

OMG, Thank the heavens for Nancy Pi!!! You have restored my faith in math! I love it and was feeling very discouraged because I wasn't getting it. Watching your clear, step by step videos has brought it all back for me. Thank you Nancy!!

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Beauty and brain in one place. A rare sight indeed. Thanks Nancy

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Perfect sentence😊

[@EyeLean5280]

THANK YOU! I've watched several videos by other teachers and professors and none of them wrote out the steps, like you have here right in the beginning - SO helpful!

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I thought I'd never be able to do these. This was extremely helpful!

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Bruh this is the 3rd time I come back to this Video in the last 4 years Nancy u are a lifesaver

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tysm its hard to learn in online school and this is the only video that truly helped :)

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Coming out with all these videos before my finals bless you

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Are u in college doing this? Or highschool

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Thank you so much for taking your time to help others this video helped me out so much. Now I feel I can be successful in college algebra at jersey college.

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Can I just say this video is the most helpful one out there! Love it!

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giiiiiirl you helped so much, thanks!!!

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True

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Hii

[@kyrajenkins1747]

I spent the past week struggling so hard with this and now I understand so quickly. I literally love you thank you so much, hopefully I won't fail another quiz!

[@noah.kosta1]

Thank you for this, doing math assignments that are late because I didn’t know how to do it, but thanks to you I do now❤️

[@keekli9046]

I love how u lay things out!

[@adorastarmach9376]

I wish you were my teacher in school. Thank you so much🙏You helped me more than you know.

[@norah496]

damn she is lefty and is writting backwards!!!

[@nidoruzi]

lmao it’s flipped. she’s not writing backwards

[@mathisfun8797]

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[@andrewmcnamee5454]

its just glass bro

[@norah496]

@@andrewmcnamee5454 ah me so dumb lol

[@shivinchauhan5699]

Almost 9years later since i studied maths in school, this video for the 1st time in my life explained solving equations so lucidly that i can't thank you enough Nancy

[@sanroom]

Thanks found it very helpful. Wrote it down step by step. back in school at 56 so I have forgotten so much and felt overwhelmed and anxious. I've always hated math so many thanks

[@Regular_Decorated_Emergency]

Great for you!!

[@madeleinephipps8334]

Thank you Nancy, my professor went over so fast in class so I didn’t get it but your explanation is really helpful!

[@Tata_1818_]

TMR is my final and this is the only thing I struggle on.. so I’m so thankful I found this video you teach better than my teacher

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This is literally the one thing that i literally cannot do!! And you helped so much you explain everything very intricately and you make it simple. Thank you so much i fr had to do this hw over 6 times

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I knew all my confusion would be gone after watching this video, and I wasn’t wrong. Thanks for helping again☺️been watching those videos for almost four years now, saved my ass countless times

[@animestudios9078]

Good teacher

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Good

[@brittm8068]

Thank you Nancy! I know that this might be over 2 years too late but your videos really helped me out because later in the school year I will be taking my EOC!

[@ryansheridan1290]

You make the equations easy to solve. Well spoken, clearly defined problems and solutions. My ERAU instructor linked us to this video, very pleased. Thank you!

[@nicolekline8251]

This is great and so helpful! Thank you for making this :)

[@michealscott4434]

Thank you so much! I understood your video, unlike my math class at times! :)

[@313pookie313]

This time, I really had to pay attention, and Nancy says it plain and simple in a way I can easily grasp it. Thanks

[@rebeccamolnar1757]

Nancy, I loved your video because you are very detailed in your teaching. Awesome!

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Nancy, you rock. Thanks for doing this!! BIG help

[@linettgidai2950]

Hi! I am in year 9, and I was blocked in these topics for a while. I didn't really get closer but now, as I watched this video, it helped me a lot. SO thank you. I love the way u explain, you are very clear with what you wanna say and speak English in a very nice way. Thank you.

[@favegossipgirl]

THIS WAS SO HELPFUL!! YOU CLEARLY EXPLAINED WHAT TO DO WHILST THE TEACHER TOOK A WHOLE LESSON

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Thanks for your slow and cincise explanation your just the best math tutor love you all the way from Papua New Guinea may God bless you for your heart of teaching

[@roxannehaoses4548]

Finally, you are an angel sent from above by the math gods. Thank you very much..

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I LOVE THE WAY YOUR DOING NANCY ..YOUR HELPING SO MUCH.. THANK YOU SO MUCH.. PLS DO MORE VIDEOS..

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You're*

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@@Asif-jt2hk grammar police lmao

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Thank youuuuu so muchh for your helpful vid....... lately Im struggling solving these thingss.... but now its really easy for mee..... thanks again♥️

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Nice. Steady paced and easy to follow. Keep encouraging.

[@mikamalikaslanov7146]

Everyone: pays attention to the math that she's explaining Me: Trying to figure out how she's writing backwards so neatly

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Not really m8 its the other way round

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dude i sat in a 2 hour class tryna learn this, and i just learned it in under 20 minutes, this is why i hate school. thankfully i can find vidoes like these

[@chidiekweonu]

Best tutorial ever. Thanks Nancy

[@Neyobe]

I FINALLY UNDERSTAND! THANK YOU NANCYYYY

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OH MY GOD THANK YOU SO MUCH BEEN STUCK FOR SUCH A LONG TIME!!!!

[@botteu]

Thank you for bringing up these special cases 🙏 I was tearing my hair out yesterday trying to solve similar problems. Great explanation 👍

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I missed the lessons by the time my mathematics teacher was explaining this,but am glad that she has really helped me.

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Watched this to complete my math assignment. Thank you for helping!

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You helped me with math in high school and now in college haha. Thank you! girl you are heaven sent.

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2 years from the future thank you so much ❤

[@mrblueskies3]

I'm taking a math class that I should have taken in high school and this was very helpful. Thank You. Also, my ADHD could not help but focus on the fact that you are a fellow lefty and you have to write backwards. Great quality video! Subscribed!

[@jin-jq5np]

me too 🥲

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Nobody: Math:iNfInItLeY mAnY sOlUtIoNs

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Infinitely many solutions = Infinite number of explosions in my brain, makes sense

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If you need an I.M.S. I just made a video about it!

[@Chlomary]

I want to thank you. I have been struggling with a teacher that doesn't want to teach and you saved my butt.

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i love the way you teach nancypi

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who else is watching this *full volume mid test?*

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Angela Mosby How?

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Wtf??😂

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No one you moron

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I am

[@jm1182]

Thank god, finally a pretty math teacher and the name Nancy pi perfect. God bless you Nancy.

[@introverteee]

not even 2 minutes in and I already know exactly what to do! thanks a lot this reallly helped :D

[@SR337]

your teaching method is amazing and easy to follow and understand, I'm watching your videos because I can understand my teacher's teaching method.

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woah! this what i was looking for thanx this helped me a lot

[@SnakesAndRoses108]

I have a math test coming up this Tuesday and this video was really helpful. I am leaving a like...

[@vincentortega4284]

Hi Nancy, excellent explanation, and very clear. Thank you so much. God bless you.

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Thank you so much for this😁 it really helped! I got the same answer as when I used the method elimination💜💜

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Omg thank you girl😭 I needed this!! Thank you a million times you’re a legend!!

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Next upload?

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my momsphone next upload what do you mean?😂

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@@iimavyyy 2 weeks without uploading

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my momsphone YEah I’m uploading tomorrow 😂 because I’ve been busy with college :(

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@@iimavyyy oh dam

[@motivatorsound6310]

All of ur video is very helping me in my math. Last month, I got 86% for my mark. Thanks

[@martinmetz5949]

Generally this demonstrates the technic of substitution for, may be, more complicated sets of linear equations. With this easy set, it would have been easier multiplying the first equation by 4 and add the 2nd to it, eliminating Y in order to get X. (With 14 to be the common denominator of 2 and 7 we could multiply the 1st e. by 7 and the 2nd e. by 2, in order to get rid of X and get the value of Y, by subtracting the 2nd e. from the 1st. e.).

[@eqrena]

Thank you! I have a test on friday and this helped. My teacher doesn't really know how to use the online learning software.

[@croissantduck7916]

Thoroughly enjoyed your video

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I love you continue teaching us how to solve the problem of equation you teach us with much love

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you are the best teacher in the world....I understood the concept so well now..thanku

[@michaeldaniel1430]

Your video helped me a lot. Thank you so much!

[@MasterZhao]

Hi Nancy! I found that this works a little easier and w/o dealing with fractions. multiply the bottom equation by 2 and u will see it works out very nicely. I always take the easiest term that will cancel out the top/bottom term to eliminate x/y. In this case u got the best of both. 😊

[@jin-jq5np]

thank you so much i love you

[@danialraziq557]

INFINATELY MANY SOLUTIONS!!!!! THANK YOU VERY MUCH

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Thanks for this. You only realise how much of this stuff you've forgotten when you need to use it.

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Omg thank you so much I have a test tomorrow and you are the only person on KZbin I actually understand

[@lucianacantu8901]

Super grateful!!

[@swiss4ever93]

Thanx a mill, you made it so simple and easy to understand!!

[@NanoTellez]

I was going to recommend this video to my class, because your explanations are so organized and clear... But then you got to the comment about the system with infinitely many solutions, where you say that -8=-8 regardless of whatever values x and y take, so any pair (x,y) is a solution. :( Not every pair would solve the system. Only those that are on the line. I am looking for a video where students can learn that "infinitely many solutions" is not the final answer. Instead, they need to present the solutions as a dependent pair. In your example, the answer to the question of "solving the system" would be that there are infinitely many solutions, and they are of the form (4/3+2/3y,y), or (x,3/2x-4) I would love it if you switched this video for one like that, because I have a feeling you would do a great job explaining it.

[@Regular_Decorated_Emergency]

She means that there can be more than one solution.

[@NanoTellez]

@@Regular_Decorated_Emergency I know what she means, but it's not what she says. And someone who isn't already familiar with the subject will believe what she says *literally*, and come out of it with a pretty serious misconception (that in a dependent system every possible combination of x and y is a solution, which is definitely wrong).

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Understood this in just a couple of minutes thanks it was very helpful 👍👏👏

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Thanks Nancy! you rock!

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Your videos help so much because you are easy to understand

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This helped so much thank you!!

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Thanks for the video, it really helped me so much. Keep up the excellent work girl 💪

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Where were you when I was taking HS Algebra? You have a pleasant demeanor and your students should be grateful.

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Thank you. I really appreciate your help

[@samlicorish5645]

For some impressive reason, women most often seem to teach so much better than men. So many male teachers offer the easy examples. You instead chose to show the more challenging ones with fractions as well, offering a way to see the fractions' solution when it is not obvious (as in whole number / one). You offer students a way to solve these with assurances that they too can get math done. Had I had your teaching when I was young, I might've even fancied myself as a modern-day Euclid. Well done, thank you.

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Love this channel, thank you so much

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aye

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Really loved this it was so useful Thank you

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Wow you are so so so so so so better than my teacher. Thank you so much this helped me a lot. You are the best

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this was so helpful thank you so much!!

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Thankyou so much. This was so helpful

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This was super helpful.🙂 I didn't really understand what my teacher was saying in class and this video helped me understand.

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Nice way to explain Thanks

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Thank you for all the help

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Amazing channel, Astounding lessons, I approve.

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love your work