Question

I need help solving this equation using the elimination method: 8s+12t=16, 6s+9t=12

Answer 1

8s + 12t = 16
6s + 9t = 12

You want to add the bottom and top together.

Answer 2

I'm am math illiterate. So, I would add and make it 14s+21t=28?

Answer 3

why... they are the same equation...

divide the 1st equation by 4

divide the 2nd equation by 3

what do you have...?

Answer 4

2s+3t=4

Answer 5

You want to s or t terms to cancel out in either equation.

I can multiply the entire 2nd equation by -4 and the entire 1st equation by 3 in order to cancel out the s-terms.

3(8s + 12t = 16)
-4(6s + 9t = 12)

24s + 36t = 48
-24s - 36t = - 48

Now add both the equations to one-another.

Answer 6

yep... so the equations have an infinite number of solutions....

Answer 7

Campbell, the equations have no solutions...

Answer 8

as you can see with @Compassionate method.... adding the equations will give

0 = 0

Answer 9

they are the same line... if you graphed them both... they sit on top of each other... so have an infinite number of points in common...

but that's just my interpretation.

Answer 10

no solution would mean the lines are parallel... never intersect..

Answer 11

You're correct, Campbell!

Answer 12

phew... that was lucky

Answer 13

I don't know either way. I'm in an online class and the teacher is from a foreign country and didn't explain it very well!
Thank you!!!

Answer 14

Ha ha.

Answer 15

Jewels, if you need anymore help just message an Ambassador or member. We're here for ya'. ;)

Answer 16

I do have another one. I really need tutoring on all of this. This one may be done the same way but he didn't specify if he wanted us to use elimination or substitution. 4x-6y=3, 6x-4y=-3

Answer 17

It would be best to use elimination

4x - 6y = 3
6x - 4y = -3

Okay, so first you need to say, "Can I multiply my x or y terms to get them to cancel out on another?"

Well, 4x and 6x have a common factor. Do you know what it is?

Answer 18

2

Answer 19

2(4x-6y=3)
-2(6x-4y=-3)
??

Answer 20

No no, I mean, at what point do 4 and 6 reach the same number?
For example, 2 and 5 have the same multiple of 10, because they're both divisble by each other.

Answer 21

24 so it would be:
6(4x-6y=3)
-4(6x-4y=-3)
Right?

Answer 22

Right!

So we have

24x - 6y = 3
-24x - 6y = - 3

Nwo we add the terms and our xs wil cancel and we can solve for y.

Answer 23

6y=-9
6y/6=-9/6
y=-1.5 right?

Answer 24

Correct. Now take -1.5 and plug it into any of the two equations to solve for x.

Answer 25

4x-6(-1.5)=3
4x+9=3
4x+(9-9)=(3-9)
4x=-6

is that right so far?

Answer 26

Yup. Now divide by 4.

Answer 27

x=-1.5
y=-1.5

Answer 28

Right! so those are your x and y intercepts.

Now if you want to find the slope just use the slope formula.

Answer 29

That one I do know. lol. Thank you so much! I think I'm beginning to understand it a little be easier. :)

Answer 30

Yup! And that's called the Elimination Method! :)

Answer 31

Thank you!