Use substitution to

solve for x and y. And we have a system

of equations here. The first equation is

2y is equal to x plus 7. And the second equation here

is x is equal to y minus 4. So what we want to do,

when they say substitution, what we want to do

is substitute one of the variables

with an expression so that we have an equation

and only one variable. And then we can solve for it. Let me show you what

I’m talking about. So let me rewrite

this first equation. 2y is equal to x plus 7. And we have the second

equation over here, that x is equal to y minus 4. So if we’re looking

for an x and a y that satisfies both constraints,

well we could say, well look, at the x and y have to

satisfy both constraints, both of these constraints

have to be true. So x must be equal to y minus 4. So anywhere in this top

equation where we see an x, anywhere we see an

x, we say well look, that x by the second constraint

has to be equal to y minus 4. So everywhere we see an

x, we can substitute it with a y minus 4. So let’s do that. So if we substitute y minus

4 for x in this top equation, the top equation becomes 2y

is equal to instead of an x, the second constraint

tells us that x needs to be equal to y minus 4. So instead of an x,

we’ll write a y minus 4, and then we have a plus 7. All I did here is I

substituted y minus 4 for x. The second constraint tells

us that we need to do it. y minus 4 needs to be

equal to x or x needs to be equal to y minus 4. The value here is now

we have an equation, one equation with one variable. We can just solve for y. So we get 2y is equal to y, and

then we have minus 4 plus 7. So y plus 3. We can subtract y from both

sides of this equation. The left hand side,

2y minus y is just y. y is equal to– these

cancel out. y is equal to 3. And then we could go

back and substitute into either of these

equations to solve for x. This is easier right over

here, so let’s substitute right over here. x needs

to be equal to y minus 4. So we could say that x

is equal to 3 minus 4 which is equal to negative 1. So the solution to this system

is x is equal to negative 1 and y is equal to 3. And you can verify that it

works in this top equation right over here. 2 times 3 is 6 which is indeed

equal to negative 1 plus 7. Now I want to show you that

over here we substituted– we had an expression that,

or we had an equation, that explicitly solved for x. So we were able to

substitute the x’s. What I want to show

you is we could have done it the

other way around. We could have solved for y and

then substituted for the y’s. So let’s do that. And we could have substituted

from one constraint into the other

constraint or vice versa. Either way, we would have

gotten the same exact answer. So instead of saying x

is equal to y minus 4, in that second

equation, if we add 4 to both sides of this equation,

we get x plus 4 is equal to y. This and this is the

exact same constraint. I just added 4 to

both sides of this to get this

constraint over here. And now since we’ve solved

this equation explicitly for y, we can use the first

constraint, the first equation. And everywhere

where we see a y, we can substitute it with x plus 4. So it’s 2 times–

instead of 2 times y, we can write 2 times x plus 4. 2 times x plus 4 is

equal to x plus 7. We can distribute this 2. So we get 2x plus 8

is equal to x plus 7. We can subtract x from both

sides of this equation. And then we can subtract 8 from

both sides of this equation, subtract 8. The left hand side,

that cancels out. We’re just left with an x. On the right hand

side, that cancels out, and we are left

with a negative 1. And then we can

substitute back over here we have y is equal to x plus 4,

or so y is equal to negative 1 plus 4 which is equal to 3. So once again, we

got the same answer even though this time we

substituted for y instead of substituting for x. Hopefully you found

that interesting.

what software was used for this presentation? I'm a college instructor, so i'm very interested ^_^

@impdok

MS Paint, really basic stuff. He also uses Camtasia Recorder ($200) + a Wacom Bamboo Tablet ($80) on a PC.

well…when you got 2y=3, didn't you hae to make it so theres only a variable…so divide 3 by 2?

thanks

WELL

@MrDollerbill CONFUSING

what if both parts of the problem equal y?

wow u r a really good explainer. mhm that is osm sauce.

God …when my teacher explained it i could not understand 1 word, but you guys, i just wanna say thanks for this dudes. y'all ROCK!!!

You are awesome…i finally understand it. Yay!

Thanks a bunch, this is great study for cramming 😉

I can finally understand!!!!! thank you!!!!

That's it? WOWWW

Say you have a problem like that, and it's a multiple choice question and it gives you answers to choose from. Would plugging each option in work too?

Name of the program pleasee !))

thank you so much for this video!!!!! yay! now im not going to fail my test!!!!

good tutorial

I've been learning this for a month; this is the first time it's made sense in a reasonable way. thank you.

thank you

You made my hope that i can pass my math exam tomorrow

You teach better than my teacher

Who else is here because they rage quit against their teachers

I know we all are having problems with our math but when we think why are we learning this? We learn this to solve our life related problems. While, most of the people like us don't use this method b'coz we think it's hard.

McGraw hall is starting to copy your idea their tutorials are not as good and schools are required to use them

math is much more than "using the pythagoras theorem" or when i grow up when am i going to use this, its all about logic and critical thinking. which is why many people value math including universities and for people to say why am i learning math its not like im going to use it i want to be a writer – i mean yeah sure you're not going to use it firsthand but you develop higher thinking skills through the process of math

… Now i know my teacher i terrible. You make it look so easy.

i didn't really understand it

Really good stuff from what I heard in this video. But maybe take in mind the people who are colour blind and can't see some of this stuff properly…

You teach soooo much better than my teacher!! My teacher just gives us worksheets for a week and expects us to understand and i learned more from a 4 minute video than in a week in her class

Thank you so much. Don't know what would have happen if you weren't on YouTube

😀

THANK YOU SO MUCH

but all my math H.W. problems don't have anything equal x or Y. It's just a number and it's really confusing. But thanks for making it easier to understand for the most part.

i had harder versions of these

My teacher shows us how to do it ONE time then examples for a few days then new subject.

This makes me hate my teacher even more. Thanks man! Great video!

Thanks. My teacher sucks at explaining and a 4 minute free video helped me better than SCHOOL ITSELF.

THANK YOU

I was stuck trying to do my math homework, and this video beautifully explained everything so thaaaank you so much<3

When are we going to use this in real life????????????????????? like Fr

Well as you can see the answer is 3 so 4 minus 7 is 3 you only have to do is to put only 3 no solution lol.

this didn't help that much, you should add different types of problem to give the viewers a clue of how to solve them in my opinion

I never listen to my teacher in class lmao, this why I'm looking up videos

Yeah I'm a junior in high school here

How you get 3

so all substitution have an answer

im a sped help

When your teacher doesn't even teach you for your exam and tells you to go on videos instead

When your teacher doesn't even teach you for your exam and tells you to go on videos instead

Nobody told me I could just -x when theres 2x I always tried to devide by 2 this makes my life 100% simpler

what did they use to record video

My problems are much more complicated than this

Thank you so much

Cool editting

easy money! I wish I can play game in class!

I don't derstand where you got the 3 from

if you get rid of the "y" at the end of the problem solving then you do NOT get y = 3; you get 2 = 3. That makes absolutely no sense. if you get rid of y, you have to bring down the 2.

i understand this more than what my teacher discusses, thanks!

Please get a better microphone

Thks

i watched this 1million times and i still don't get it

?…….

Now I know y math is so hard…..get it?

cheers helped me understand better

i honestly feel like an idiot for being the only one in class who doesn't get this

uh, im learning this in 10th grade. also, school didnt even teach this well

Damn this was helpful

I learned more in a 4 minute video than in a week of class. My math teacher is Khan.

You need to do word problems this topic is still confuseing to me😬

I’m in 8th grade learning sophomore math😭 Thank you I finally understand it now

Despite watching this i still dont get it!

U are supposed to multiply seven times the x right not like this

My accelerated math teacher just confused everyone in the class… I’ll have to show this to my friends so we’re not lost anymore 😁.

I love you ! I was like how tf do I do this

succ

this is good for my final exam review

this doesn’t make sense

where did the -1 come from

Saved me thank you

What about a problem like

Y=-2x+13

X=9-y

THANK YOU SO MUCH 🙂

6 years late but thanks

I was so lost in my math class thanks I understand now

Thanks so much teacher

I thought this was hard in year 2… Now I'm thinking, where was khan academy back then???

Im don’t understand this

Simple questions.. no one ever goes over the hard ones. Awesome

Yeah um can you like do more problems then one please

My teacher gets mad at me for not understanding

THANK GOD FOR KHAN ACADEMY

nani

Anyone know how he got -1 at2:29

He lost me at y+3 someone tell me where it came from. He had me till he said that

In math class lol

Anyone here Attention Deficit and can't pay attention, like, at all? :')

I knew that already just tell me how to do y=5x+6 y=6x+10 or any other duos like this one for subsitutuion

Can someone help my question is -4x + 5y = 40

X = 2y – 13

Don't UNDERSTAND!!!!!

😣😣😣

Thank you khan academy.

Thank you, i had no idea what the teacher was saying at school but watching this video I understand now!

What program are you using to write the equations on?