Question

need help solving with elimination method.
8s+12t=16
6s+9t=12

Answer 1

Hint: Simplify both equations first.

Answer 2

Notice that if we divide the first equation by 4 and the second equation by 3, we can simplify both equations to this:

2s + 3t = 4
2s + 3t = 4

Answer 3

m horrible with math I have no idea how and im so confused

Answer 4

I understand.

Answer 5

thank you so much for your help

Answer 6

So if we tried to use the elimination method for this particular problem, we would end up with 0 = 0. Anytime you end up with that kind of result, it means that the solution to the system is all points (s,t) on either line.

Answer 7

If that confuses you, just remember that when we simplified both equations, we ended up with:

2s + 3t = 4
2s + 3t = 4

which essentially means that both equations represent the same line. Therefore they both must have the same solutions.

Answer 8

ok It makes a little sense on how you put it thank you

Answer 9

I have one more if I post it do you mind helping me understand it? its using the same method ;)

Answer 10

Well, unfortunately, not every system is simplifyable, and not every system will end up being representations of the same line.

Answer 11

Such cases only represent a particular class of systems of equations.

Answer 12

Namely "equivalent" equations.

Answer 13

You will either have one of the three things:
1. a NORMAL system (two lines that intersect at a single point)
2. an INCONSISTENT system (two parallel lines that never intersect)
3. an EQUIVALENT system (two equations that represent the same line)

Answer 14

So you will have different approaches to each.

Answer 15

I just have problems trying to figure out what numbers to use. in the equations. now what do i do if they are not easy to eliminate like this one?

Answer 16

Show me one you think is not easy. As far as I'm concerned, according to your situation, none of them are easy.

Answer 17

ok let me post it in the question part so you get the points for helping me with it

Answer 18

Okay, but you should close the question immediately afterwards.