Question

GEEZ I DON'T KNOW the Dddition method!!! +[ hehe

Answer 1

2x + 3y = 6
5x + 2y = 4

Answer 2

add ther equations:
2x+3y+5x+2y=6+4

Answer 3

addition is not suitable here :(

Answer 4

So like dis 2x+3y+5y +

Answer 5

hmm did you mean "elimination method"?

Answer 6

WAIT HOW -.-

Answer 7

no it's adition methos..oops my bad let me change it up there
here Which of the following equations could be the result of multiplication and addition to eliminate a variable in the system of equations?

Answer 8

hmmm oook
have you covered the "elimination method" yet?

the instructions assume you already have

Answer 9

if you haven't.. well, now is a good time to page through it :)

Answer 10

I did i even reworte the examples couple times -.- but it's hard for me to consentrate on 'em

Answer 11

well... are those 2 equations the only ones given?

Answer 12

yes just 2

Answer 13

hmmm.....
ok... so...hmm one sec... .lemme .hmm write it about

Answer 14

hrmmm okay hmmmm thanks

Answer 15

\(\large \begin{array}{llcll}
2x+3y=6&{\color{brown}{ \times -2}}\implies &-4x\cancel{-6y}=-12\\
5x+2y=4&{\color{brown}{ \times 3}}\implies &15x\cancel{+6y}=4
\\\hline\\
&&???
\end{array}\)


notice
the top was multiplied by "something"
and the bottom in this case, was also multiplied by "something else"

notice what happened to the "y" variable, if you add them up vertically
what does that give you as result?

Answer 16

okay so i subtract -12 -4??

Answer 17

well, notice is -12 and +4
but yes, you'd do -> -12 + 4

and on the 1st column, you'd also do addition to -4x and 15x
that is -4x+15x

Answer 18

You want to cancel out the y's. So multiple the top by -2 and the bottom by 3.

So you will get

-4x -6y=-12
15x +6y=12

Answer 19

What does x equal?

Answer 20

so.. notice now \(\begin{array}{llcll}
2x+3y=6&{\color{brown}{ \times -2}}\implies &-4x\cancel{-6y}=-12\\
5x+2y=4&{\color{brown}{ \times 3}}\implies &15x\cancel{+6y}=4
\\\hline\\
&&11x+0y=-8
\end{array}
\\ \quad \\
11x=-8\implies x=-\cfrac{8}{11}\)

notice, we got "x", by "eliminating" one variable, that is, "y"

Answer 21

@jdoe0001 You are confusing her by not multiplying 3 and 4.. You are wrong.

Answer 22

hmmm hold the mayo

Answer 23

shoot, you're correct, I missed a couple of ....lemme redo that quick

Answer 24

@AloneS Do you understand any of this?

Answer 25

Example:

\(\color{#000000 }{ \displaystyle 2x+3y=9 }\)
\(\color{#000000 }{ \displaystyle 3x+2y=1 }\)

You can multiply the first equation times some number, and second equation by another number. (When I say "multiply equation times the number = multiply every component in the equation times the number".)

I can multiply the first equation times 3,
and the second equation times -2.

\(\color{#000000 }{ \displaystyle \color{red}{(}2x+3y=9\color{red}{)\times 3} }\)
\(\color{#000000 }{ \displaystyle \color{red}{(}3x+2y=1\color{red}{)\times (-2)} }\)

\(\color{#000000 }{ \displaystyle \color{red}{(}2x\color{red}{)\times 3}+\color{red}{(}3y\color{red}{)\times 3}=\color{red}{(}9\color{red}{)\times 3} }\)
\(\color{#000000 }{ \displaystyle \color{red}{(}3x\color{red}{)\times (-2)}+\color{red}{(}2y\color{red}{)\times (-2)}=\color{red}{(}1\color{red}{)\times(-2)} }\)

\(\color{#000000 }{ \displaystyle 6x+9y=27 }\)
\(\color{#000000 }{ \displaystyle -6x+(-4x)=-2 }\)

Add the equations. (Add \(x\)'s to \(x\)'s, \(y\)'s to \(y\)'s, and number to number.)

\(\color{#000000 }{ \displaystyle~6x~~~+~~~9y~~~=~~27 }\)
\(\color{#000000 }{ \displaystyle -6x+(-4x)=-2 }\)
\(\color{#000000 }{ \displaystyle ^\text{_______________________} }\)
\(\color{#000000 }{ \displaystyle~0x~~~+~~~5y~~~=~~25 }\)

Notice, the \(x\)'s canceled. You remain with:

\(\color{#000000 }{ \displaystyle 5y=25 }\) (divide both sides by 5)
\(\color{#000000 }{ \displaystyle y=5 }\)

You can use one of the equations to solve for \(x\), once you found the \(y\).
\(\color{#000000 }{ \displaystyle 3x+2y=1 }\)
\(\color{#000000 }{ \displaystyle 3x+2\cdot \color{blue}{5}=1 }\)
\(\color{#000000 }{ \displaystyle 3x+10=1 }\)
\(\color{#000000 }{ \displaystyle 3x+10\color{red}{-10}=1\color{red}{-10} }\)
\(\color{#000000 }{ \displaystyle 3x=-9 }\)
\(\color{#000000 }{ \displaystyle x=-3 }\)

So you get:
\(\color{#000000 }{ \displaystyle x=-3 }\)
\(\color{#000000 }{ \displaystyle y=5 }\)

Answer 26

\(\begin{array}{llcll}
2x+3y=6&{\color{brown}{ \times -2}}\implies &-4x\cancel{-6y}=-12\\
5x+2y=4&{\color{brown}{ \times 3}}\implies &15x\cancel{+6y}=12
\\\hline\\
&&11x+0y=0
\end{array}
\\ \quad \\
11x=0\implies x=0\)

Answer 27

You shouldnt be giving her the answer like that. You should be allowing her to assist by solving it.

Answer 28

Wait so jdoe is wrong O.O

I'LL FOLLOW @SolomonZelman since it looks right<3

Answer 29

@Destinyyyy covered that already, thus

Answer 30

@SolomonZelman gave an example.

Answer 31

Are you still looking for help?

Answer 32

ooh yea ..i still do -.-

Answer 33

well, I missed one digit, yes

anyhow, notice the idea
the top gets multiplied by -2, so we'd end up with a -6y
the bottom gets multiplied by a 3, so we'd end up with a +6y
-6y + 6y = 0, thus "eliminating" one variable, and solving for the other

so, our aim in the multiplication, was to eliminate "y" all along

Answer 34

I can help you.

Answer 35

Do you understand any of this so far? Or would you like to start at step one?

Answer 36

I dont want to give you the answer and then you go and take a test later and have no clue what your doing.

Answer 37

true destiny ...can you show me again i was looking thrue @SolomonZelman example and it kinda makes sence....wait is doe doing it right?? I'm so confused

Answer 38

Alright..

Answer 39

2x +3y =6
5x +2y =4

So first you want to eliminate the x’s or the y’s. Addition is elimination.

So lets eliminate the y terms. To do that we need to find what 3 time 2 equals.

-2(2x +3y =6)
3(5x +2y =4)

Can you solve that out?

Answer 40

He kind of was but its a mess.

Answer 41

Let me try So do i subtract the numbers in perenthesis

Answer 42

You should be getting ride of the parenthesis by multiplying each number..

So -2 to each number in the first line and 3 to each number in the second line.

Answer 43

Like distributive property.

Answer 44

So your original equation should look different.

The top line should now be

-4x -6y =-12

What will the second line be?

Answer 45

???

Answer 46

Have you figured it out or..?

Answer 47

oKA so i distrubute the first one -4x -6y =-12

Answer 48

Yes!

Answer 49

ooh here x=−3/2y+3

Answer 50

Nope.

Answer 51

Sole the second line first. Then line them up. (top to bottom)

Answer 52

Solve *

Answer 53

like this 2x+3y=6
5x+2y=4

Answer 54

Yes you will line them up like that..

-4x -6y= -12
<---- fill in the second line here after you distribute

Answer 55

-4x -6y= -12
15x +__y =____

Answer 56

3 times 5= ___ --->> __x
3 times 2= ___ --->> __y
3 times 4=___--->> ___

Answer 57

Are you still wanting help? I need to get back to my accounting class soon.

Answer 58

wait i'm writing it all down on the paper i think i got it ! let me see

Answer 59

Okay.

Answer 60

thansk i wish i could medal you twice<3

Answer 61

whats your answer?

Answer 62

You're welcome. If you need any more help tag me.

Answer 63

Of Coarse i will thank you soo much!!<33