Farrar Posted September 18, 2017 Share Posted September 18, 2017 (edited) nm Edited September 22, 2017 by Farrar Quote Link to comment Share on other sites More sharing options...
Arcadia Posted September 18, 2017 Share Posted September 18, 2017 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 5 Quote Link to comment Share on other sites More sharing options...
wapiti Posted September 18, 2017 Share Posted September 18, 2017 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. 1 Quote Link to comment Share on other sites More sharing options...
Farrar Posted September 18, 2017 Author Share Posted September 18, 2017 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? Quote Link to comment Share on other sites More sharing options...
Arcadia Posted September 18, 2017 Share Posted September 18, 2017 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 4 Quote Link to comment Share on other sites More sharing options...
RootAnn Posted September 19, 2017 Share Posted September 19, 2017 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 2 Quote Link to comment Share on other sites More sharing options...
8filltheheart Posted September 19, 2017 Share Posted September 19, 2017 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. :) 4 Quote Link to comment Share on other sites More sharing options...
Farrar Posted September 19, 2017 Author Share Posted September 19, 2017 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. Quote Link to comment Share on other sites More sharing options...
RootAnn Posted September 21, 2017 Share Posted September 21, 2017 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.) Quote Link to comment Share on other sites More sharing options...
regentrude Posted September 21, 2017 Share Posted September 21, 2017 (edited) Please don't skip it. 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 September 21, 2017 by regentrude 3 Quote Link to comment Share on other sites More sharing options...
Farrar Posted September 22, 2017 Author Share Posted September 22, 2017 (edited) nm Edited September 22, 2017 by Farrar Quote Link to comment Share on other sites More sharing options...
Arcadia Posted September 22, 2017 Share Posted September 22, 2017 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.It’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? 3 Quote Link to comment Share on other sites More sharing options...
Farrar Posted September 22, 2017 Author Share Posted September 22, 2017 We pretty much already did what RootAnn suggested and skimmed over it pretty quickly. So it's a done deal. 1 Quote Link to comment Share on other sites More sharing options...
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