Algebra

[stark apex]

Anyone able to help explain how to do this to me? My teacher has an accent and I can not understand very well. I have a test next week and I am lost. 😭 🙏

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[stark apex]

Simultaneous equations using elimination

No idea what to do

[honest lark]

Which part?

Do you want me to demonstrate just one?

And you can do the rest?

[stark apex]

Yea please

Just once I know how to do 1 I should be able to do the rest

[honest lark]

ok, I will demonstrate Q2 since Q1 is too easy and won't give a proper idea of how to do the rest

[stark apex]

Okay

[honest lark]

So, we have $5x+y=23$ AND $2x+y=11$ and we are supposed to find $x,y$ that satisfy these equations

[covert pine]

wolfqz

[honest lark]

Do you understand what the term "coefficient" means?

[stark apex]

Teacher mentioned it but she never explained it

So no

[honest lark]

okay so basically

youknow how x and y are variables right?

[stark apex]

Yes

[honest lark]

alright

in the equation 5x+y=23

there are x,y variables

the "coefficient" of x is 5

[stark apex]

Ohh okay

[honest lark]

as you can see, it is just the constant term multiplied with x

[stark apex]

Yes

[honest lark]

okay, can you tell me coeff of x in 2x+y=11?

and what about the coeff of y?

[stark apex]

isn't y just 1

and x is 2?

i might be stupid

[honest lark]

Yes

youre correct

THOSE ARE THE COEFFICIENTS

not the values

[stark apex]

Oh thank god

o

wym

did i say value or coefficients

[honest lark]

yaahh u said neither so it's generally assumed u meant values

but it's okay

u said the correct coefficients

[honest lark]

anyways, you realize that if we multiply both sides of an equation by the same number, then the equation is equivalent to the original

[stark apex]

uhh....

[honest lark]

for example

the equations 2x+y=11 and 4x+2y=22 are the same equation

[stark apex]

yea

[honest lark]

yea that's what i was saying

[stark apex]

oh okay

[honest lark]

what happens if u multiply both sides of 2x+y=11 by 5?

[stark apex]

10x and 5y?

[honest lark]

10x+5y=(what?)

[stark apex]

55???

[honest lark]

yesss

10x+5y=55

[stark apex]

Oh word

[honest lark]

what if we now multiply both sides of 5x+y=23 by 2?

[stark apex]

10x + 2y = 46

[honest lark]

PERFECT

10x+5y=55
10x+2y=46

[stark apex]

Okay that makes me feel way better

[honest lark]

We have this two equation

What if we just subtract this two equations?

[stark apex]

55 - 46?

[honest lark]

And the left hand side?

[stark apex]

don't the 10x cancel each other out

and 5y - 2y = 3y

so 3y = 9?

i might be a lost cause

[honest lark]

Bro wwhat

What u did is perfect

3y=9

so y=3

[stark apex]

yeah

Oh wait fr

[honest lark]

Fr

Can u find x, knowing y=3?

[stark apex]

No?

[honest lark]

Look at the original equations. Pick one of them, say 2x+y=11.

We know y=3.

[stark apex]

2x + 3 = 11

[honest lark]

So we found x as well.

[stark apex]

so 11 - 3 = 8

divide by 2 to get x

[honest lark]

2x=8 yes then x=4

[stark apex]

x = 4?

[honest lark]

yes

yes

[stark apex]

yess

[honest lark]

NOW

LETS SUMMARIZE WHAT WE DID

[stark apex]

Okay

[honest lark]

$5x+y=23$ AND $2x+y=11$

[covert pine]

wolfqz

[honest lark]

we multiplied both these equations with some constant

But the constants were very special

They made the coefficient of x the same

And when the coefficients were the same, we just subtracted the equations

[stark apex]

5x - 2x?

[honest lark]

BECAUSE when the coefficients were the same, we knew subtracting the equations would lead to one of the variables being eliminated

[honest lark]

Yes, u can also do that

[stark apex]

yes

[honest lark]

I was getting to that

[stark apex]

o

[honest lark]

That rn what we did was ELIMINATE x

[stark apex]

sorry

[honest lark]

We can also ELIMINATE y

[honest lark]

noworries, it was pretty smart of u to notice that actually

[stark apex]

that just looked like common sense to me.

collect the like-terms

[honest lark]

Yes

[honest lark]

In this case, we can also subtract these equations directly thus eliminating y

Can you try Q3 now, just tell me what answers u get after solving them and i'll confirm if u did it correctly or not

[stark apex]

okay do you want me to type the working out here

so you can see where i go wrong

if i do*

[honest lark]

first, just type the answer

[stark apex]

okay

[honest lark]

if it's right then i don't require a working out

ofcourse just write it in ur exam 🔥

[stark apex]

2x + 3y = 3
5x + 3y = 12
(so I dont have to go back to the top)

im lost sorry 🙏

i tried 5x - 2x

[honest lark]

show ur working

or what u've tried

[honest lark]

Then?

[stark apex]

3y + 3y

6y

[honest lark]

What

subtract the equations will eliminate y

[stark apex]

no idea man

[honest lark]

because it will be 3y-3y

5x+3y-(2x+3y)=12-3

[stark apex]

wait, i am so sorry I gotta go eat my food 🙏

[honest lark]

no worries

[stark apex]

i will be back in no more than 30 mins

[honest lark]

ping me when ur back

[stark apex]

okay

sorry for this 😭

[stark apex]

I'm back @honest lark

again, sorry for having to go.

I only got like an hour until I have to go

[honest lark]

ok no worries @stark apex

[honest lark]

read this

ts subtracting the equations

the - sign distributes

5x+3y-2x-3y=9

[stark apex]

why do you minus the 3y by 3y

[stark apex]

.

[honest lark]

So that we can get rid of y

[stark apex]

ah ok

[honest lark]

Since we already know how to solve an equation in one variable

So we will convert a problem with two variables and two equations into a one variable

[stark apex]

so 5x - 2x basically?

[honest lark]

yes

that's 3x

=9

[stark apex]

3x = 9?

[honest lark]

yesshh

[stark apex]

yeah

x = 3 ?

[honest lark]

yesh

and y=?

[stark apex]

no idea ngl

is it negative?

cause 2x + 3y = 3

and if x is 3

😭

[honest lark]

Yes

What exactly

[stark apex]

wouldn't y = 1

2x = 6

[honest lark]

y=-1 you mean

[stark apex]

oh ye whoops

[honest lark]

yesh

nice

you solved this

try the next

[stark apex]

3m - 4n = -18
5m - 4n = -22

we eliminate n right

or m

can be either

[honest lark]

sure

eliminating n seems easier

but it can be either

[stark apex]

yeah

[honest lark]

to eliminate m you will have to multiply the first eqn wtih 5 and second with 3

to eliminate n u just have to subtract

[stark apex]

5m + 4n - 3m - 4n?

n cancel each other out

im shocking

[honest lark]

Nice

[honest lark]

What's the other side

[stark apex]

2m

[honest lark]

What

Yes

But the other side

[stark apex]

o

[honest lark]

WAIT

how did u get to this

[stark apex]

I did what you did before.

[honest lark]

i mean it's the correct expression but the ordering is a bit off so im scared u didnt subtract properly

[honest lark]

5m-4n-(3m-4n)=-22-(-18)

[stark apex]

Ok

[honest lark]

5m-4n-3m+4n

yes

now solve

[stark apex]

can you give me a tip on what to do next

[honest lark]

wdym

you hve 2m=-22+18

[stark apex]

wait

[honest lark]

2m=-4

[stark apex]

Huh

22 - -18?

[honest lark]

-22-(-18)

so -22+18

(-1)(-1)=+1 remember

[stark apex]

yeah

two negative = one positive

[honest lark]

yeah

exactly

so can u continue

with this

and the next parts too?

[stark apex]

22 + 18 right

40?

oh wait

-22 + 18

-4

2m = -4

[honest lark]

YEs

GOOD

[stark apex]

oh your back

I have to go in like 10 minutes

I will be back tmrw but like, you don't have to help if you don't want to.

Like alg

[honest lark]

i was taking a shower bruh

🥀

[stark apex]

Yeah just saying tho

I have to go pretty soon, but like if you don't want to alg.

[raven bison]

@stark apex

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[stark apex]

+close

[raven bison]

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[raven bison]

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