Question

y = 1/2x - 6
2x + 6y = 19

Can you show me both Elimination and Substitution method?

Answer 1

We'll start with the substitution method...you know what y = since y = 1/2x - 6

so just substitute that into the second equation wherever you see a 'y'

2x + 6(1/2x - 6) = 19

can you solve this for 'x' ?

Answer 2

2x + (3x - 36) = 19

Am I doing this correctly..?

Answer 3

You are indeed :)

Answer 4

So then do I add 36 onto the -36 and 19?

Answer 5

Yes add 36 to both sides... so then you will have

2x + 3x = 55

And from there...?

Answer 6

6x = 55

Answer 7

wait 5x I mean

Answer 8

So x would equal 11

Answer 9

that is correct! now that you know what x equals...go back into either original equation and plug in x = 11...and solve for y...

lets do the second one...

2x + 6y = 19
becomes
22 + 6y = 19

Solving for y we get...?

Answer 10

Well you would subtract 22 on both sides, so it would be
6y = -3 ...?

Answer 11

Right....so what does y = ?

what is -3 / 6 ?

Answer 12

-0.5 ?

Answer 13

Right! lets keep it as a fraction though...so

x = 11
y = -1/2

Okay ready for the elimination method?

Answer 14

Yeah, I am. I didn't realize how easy that was.

Answer 15

lol yeah they are simple :) ...well actually...do you know the elimination method? if you do....do this out for me since you know the answers you SHOULD get...want to do this one and let me know what you get? or should we do it out here?

Answer 16

Actually the elimination method is more difficult for me. Can we work it out..?

Answer 17

Absolutely :)

Answer 18

Actually, I have to go eat. Can we continue this in like 20 minutes..?

Answer 19

haha sure I'll still be around :)

Answer 20

Alright thanks ^-^

Answer 21

Back c:

Answer 22

How was dinner? lol

Answer 23

Oh delishh c: Thank you ^-^

Answer 24

lol of course :)

so okay ready for the elimination method?

Answer 25

Yes, sir c:

Answer 26

Hang on it's a lot to type lol

Answer 27

Haha no worries, take your time c:

Answer 28

y = 1/2x - 6
2x + 6y = 19

Lets line up the variables...

y = 1/2x - 6
6y = -2x + 19


Okay that looks better... so now we want to eliminate one of these variables...doesn't matter which one...lets choose 'x'...so multiply the top equation by 4

4y = 2x - 24
6y =-2x +19

Now we want to combine (add) these 2 equations...

4y = 2x - 24
+ 6y = -2x + 19
----------------

4y + 6y = 10y right?
2x - 2x = 0 right?
and
-24 + 19 = -5 right?

so we have

10y = -5

y = what ?

Answer 29

Tell me if there is anything you don't get...

Answer 30

So would y equal -1/2? Or did I divide it wrong?

Answer 31

No you got it right :)

make sense? what did we find y to equal in the substitution method? -1/2 ...so we are on par here :)

Answer 32

Yeah it makes sense, oh I see.

Answer 33

Alright...so to solve for 'x'...what would we do? any idea?

Answer 34

Don't we replace the y, with the answer we got?

Answer 35

You're thinking of the substitution method again :P

nope we need to do the entire process over again and solve for 'x' this time lol

Answer 36

Oh lord /.\ Bring it on xD

Answer 37

lol Okay...

y = 1/2x - 6
6y = -2x + 19

Now you tell me...how would we eliminate the 'y' variable this time?

Answer 38

Multiply by 6 on the bottom equation, correct?

Answer 39

You mean the top equation right? if you did the bottom there would be

y = 1/2x - 6
36y = -12x + 114

not quite :)

Answer 40

Wow this is not adding up for me...okay hang on lol...

Answer 41

Haha, yeah I was looking at it

Answer 42

alright so

y - 1/2x = -6
6y + 2x = 19

multiply the top equation by -6

-6y + 3x = 36
6y + 2x = 19

add the 2 equations...

-6y + 3x = 36
+ 6y + 2x = 19
---------------
5x = 55

ahh there we go...don't know why I kept messing up lol

Answer 43

So yeah, then x would equal 11 c:

Answer 44

yeah lol....apparently on paper I can't work correctly lol...

but yes x would = 11 lol

and there we have both methods...obviously if you can....substitute haha :)

Answer 45

Ah god,

Answer 46

You helped me so much

Answer 47

Glad to do so :) hope everything was understandable :)

Answer 48

Very c: Thank you so much!

Answer 49

Anytime :)

Answer 50

I have another one, but I might finish it tomorrow xD And it seems more understandable so c:

Answer 51

But I have to go, thanks again!

Answer 52

Alright if you can't get it feel free to message me on here :) have a good night :)