# nm

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nm

Edited by Farrar
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honestly - I don't think I've ever solved a set of equations by adding them together or subtracting one from the other.

I have and so have my older boy during exams. The method of substitution can sometimes lead to messy fractions and some simultaneous equations are just obvious enough that adding or subtracting one from the other would solve for one unknown immediately.

For example if I have a set of simultaneous equations such that

3a + 4b = 16

3a - 4b = 8

So if I add, 6a = 24, a=4

If I subtract. 8b = 8, b = 1

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I would definitely not skip it.  At most, you might combine the addition and subtraction sections into a single lesson.  I think it's a pretty important method for solving systems, including multiplying to get one or both equations to a state in which they can be added or subtracted in order to eliminate.  (as for substitution, eww)  I'm sure it's hiding in Dolciani someplace as well.

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Yeah, in that case it's obvious - and that's what every problem was basically - ones where it was almost too pat. It felt impossibly simple, if that makes sense. But if I solved by substitution, I wouldn't get messy fractions... it would just take slightly longer... If the answer is a messy fraction, isn't it just going to be one no matter how you solve it? What am I missing with that?

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If the answer is a messy fraction, isn't it just going to be one no matter how you solve it? What am I missing with that?

I meant substitute leads to messy fractions. For example with the very obvious example I use above,

3a + 4b = 16

3a - 4b = 8

If I put a in terms of b to substitute using the first equation,

a = (16/3) - (4/3)b

Then putting that into the second equation,

3(16/3) - 3(4/3)b -4b = 8

16- 4b - 4b = 8

8b = 8

b = 1

a = (16/3) - (4/3)(1) = 12/3 = 4

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Hm. I use the addition/subtraction thing all the time. Saw it in Foersters Alg 2 a bit, too. Haven't made it to that Jacobs chapter yet, so I don't know how tedious it is.

4x + 3y = 8

-2x -    y =-2

Multiply the second equation by 2, then add both together.

4x + 3y = 8

-4x -  2y =-4

-------------------

y = 4

x =-1

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I wouldn't skip it either.  Linear combinations with 3+ variables are probably in their future (at least it has been in all of my kids'.)   When they learn matrices, it is cleaner than linear combination, but understanding linear combination leads to easy understanding of matrices.

w -   5x + 2y -    z = -18

3w +   x -  3y + 2z=   17

4w -  2x +  y -    z =   -1

-2w + 3x - y +  4z=    11

FWIW, this is one of the word problems my dd solved today using linear combination in alg 2: The road from Tedium to Ennui is uphill for 5 miles, level for 4 miles, then downhill for 6 miles.  John Garfinkle walks from Ennui to Tedium in 4 hrs; later he walks halfway from Tedium to Ennui and back again in 3 hrs 55mins,.  Still later he walks from Tedium all the way to Ennui in 3 hrs and 52 mins.  What are his rates of walking uphill, downhill, and on level ground, if these rates remain constant.

Linear combinations do have value.  :)

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Well, I wasn't going to skip it - I said skim... I'm still a bit torn about doing that. It was just so much more rote than most of Jacobs and for four sections and a kid who works sloooooow.

We'll see. We had a day off today.

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Ok, I looked at this today. Looks like it is at the start of Chapter 7 and it spends three sections on solving simultaneous equations by addition & subtraction. With a kid who was quick on the math uptake, you could cover all three sections in one sitting, IMO. Then, you could just pick & choose which problems from each section to do - or just do all of Ch 7-3 Set 1 & 2 (or 1 & 3, or 1, 2 & 4, or 1, 3, & 4).

My dd#2 will need all three sections explained separately over three days. DD#1 probably could have handled it in one day with two days of practice before it went into rotation for continued practice & review. (She didn't use Jacobs.)

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It makes many problems so much quicker to solve, and comes up often in physics (for example Newton's laws with coupled objects). Students who have not been taught to solve systems of equations by this method are at a disadvantage. Sigh. I wish I did not have to reteach my college students basic algebra.

Edited by regentrude

nm

Edited by Farrar
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I sort of hate how me saying I was thinking about breezing through this to skim it became that I was trying to skip it. Sigh.

Itâ€™s what was written in your first post that I quoted below that makes it sounds like you are thinking of skipping that section.

So... I'm debating skimming over some stuff in Jacob's and I'm trying to decide if any of it really matters.

...

I'm tempted to skip it, but I'm also getting to the math where I'm less expert - I feel plenty competent, but is there some reason that this is the foundation for something down the road that I'm not getting?

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We pretty much already did what RootAnn suggested and skimmed over it pretty quickly. So it's a done deal.

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