Question

Use either elimination or substitution to find the solutions (if any).
2y + 3x = 7 and 8y + 12x = 28

Answer 1

Let's do this together! Ready?

Answer 2

ok

Answer 3

oh hi uber

Answer 4

Equation 1 = (2y + 3x = 7)
Equation 2 = (8y + 12x = 28)

What I like to do first is mix the equations around to get them in the form of
x= blahblah or
y = blahblah.

Equation1y =
(2y + 3x = 7)
2y = -3x +7
y = (-3x + 7)/2

Equation1x =
(2y + 3x = 7)
3x = 7-2y
x = (7-2y)/3

Let me know when you're ready and I'll tell you what we should do next.

Answer 5

Hi there, boog1!

Answer 6

Just lemme know whenever you're ready to do the next step. Also, after we solve this, I'll also explain the elimination method.

Answer 7

so which are we using elimination or substitution

Answer 8

ok so now we take x=97-2y)/3 an and it to the second equation?

Answer 9

That's right. For now we're doing substitution.

Answer 10

9=(

Answer 11

i kinda know that one

Answer 12

8y + 12[(7-2y)/3]= 28

Looking good so far?

Answer 13

yup i got that far

Answer 14

Okie dokie. Now, this part is really ugly:
12[(7-2y)/3]

Answer 15

lol

Answer 16

What I would do is distribute the /3.

Answer 17

So,
[(7-2y)/3]
becomes:
7/3 - 2y/3

Answer 18

ok

Answer 19

8y + 12[7/3 - 2y/3]= 28

Answer 20

Now, we distribute the 12.

Answer 21

8y + 84/3 - 24y/3 = 28

So far so good?

Answer 22

ok

Answer 23

Do you see anything we can do to make the equation less complicated?

Answer 24

8y+28-8y=28?

Answer 25

Excellent.

Answer 26

Hmm... an interesting conundrum...

Answer 27

then we take the 8y out because there is 2?

Answer 28

You see what our problem is, right?

Answer 29

Yup.

Answer 30

Hahah.... I just noticed something funny.

Answer 31

Equation 1 = (2y + 3x = 7) Equation 2 = (8y + 12x = 28) What I like to do first is mix the equations around to get them in the form of x= blahblah or y = blahblah. Equation1y = (2y + 3x = 7) 2y = -3x +7 y = (-3x + 7)/2 Equation1x = (2y + 3x = 7) 3x = 7-2y x = (7-2y)/3 Let me know when you're ready and I'll tell you what we should do next.

Answer 32

So we end up with 0=0, right?

Answer 33

so y=28

Answer 34

NooooooooOOoooo :P

Answer 35

"8y+28-8y=28?"
28 = 28
0=0

Answer 36

You know what this means?

Answer 37

not really

Answer 38

Hint: because we have no "X = something" or "Y = something", this means one of two choices:

"Unlimited answers"
or...
"Not a real equation"

Answer 39

ok this is the next question for this problem
. For equation ___________
1. The x-intercept is ___.
2. The y-intercept is ___.
3. The slope is ___.

Answer 40

The way to find this out is to see whether the last sentence we're left with is true or not.
So... if you ever got something like 0 = 5, you know that's a false, so there are 'no solutions"

So tell me what our answer is.

Answer 41

0

Answer 42

this is unlimited answers

Answer 43

It's not zero, though. Remember, it's only 0 if it says "y=0" or "x=0". What we got was "8y-8y+28=28". Which turns into "28=28", which you can turn into "0=0"

Answer 44

Excellent! Unlimited answers. Now, if it's unlimited answers, what does this tell us about the two lines?

Answer 45

they will be paraell

Answer 46

If they're parallel, this actually means "no answer exists".
An "answer" is when the two lines touch. Parallel lines never touch.

Answer 47

i am looking at my notes

Answer 48

Think of it this way: Unlimited answers means the lines are always on top of each other, right? And in a two dimensional world, what happens if two lines are on top of each other?

Answer 49

unique solution

Answer 50

Unique solution would mean that they hit only once. Let's do a quick twiddla thingy.

Answer 51

ok

Answer 52

http://www.twiddla.com/584279