Math Is Fun Forum

Au101

Member

Registered: 2010-12-01

Posts: 353

Simultaneous equations with 3 unknowns

Hi guys, I'm stuck with a really horrid set of simultaneous equations, after some working, I found out that:

Which I'm fairly sure is correct, since plugging in the answers which the answer book gives does give the right answers. Now from this, I think I'm right in saying that:

Which I simply cannot solve. Can anybody help me to solve this, or is there perhaps a simpler method which I've completely missed

Last edited by Au101 (2010-12-28 08:47:54)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Simultaneous equations with 3 unknowns

hi Au101

Yes, they're really nasty!  What did the problem start with?

edit :  Actually, I think I've spotted a short cut.  Is c = 3 by any chance?

Bob

Last edited by Bob (2010-12-28 09:07:00)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Simultaneous equations with 3 unknowns

You're a clever man Bob, how did you do it?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Simultaneous equations with 3 unknowns

hi

Call  the 1/(16a........) term D

Times both sides by D.

Then look for easy elements to equate.

eg.  first element : 16 - 7c = 5D  and middle element : 5c - 8 = -7D

Divide one by the other to eliminate the Ds and you get -112 + 49c = 25c - 40 .... find c.

Then I used 4b - 40 element and 14 - 2b element to find b.

Then a follows pretty quickly.

Remember you have got 9 equations here and only a, b and c (plus D) to find so it is not so hard after all.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Simultaneous equations with 3 unknowns

Ah thanks Bob, I'll give it a try, it just seemed that using the a,b and c terms would be easier, I didn't think to let the the determinant = D, thanks!

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Simultaneous equations with 3 unknowns

Ooooh, that's worked perfectly, thanks very much!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Simultaneous equations with 3 unknowns

hi Au101,

I didn't think to let the the determinant = D, thanks!

That's because it looked so nasty;  I thought "Let's find a way to get rid of it!"

Always a pleasure to try and help you.  How am I getting along with your matrices course?  Is there an exam at the end?

Bob

Last edited by Bob (2010-12-28 21:25:12)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Simultaneous equations with 3 unknowns

Hi Bob, thanks again. Well the A-level mathematics examinations have changed a little in recent times, but the Edexcel board currently offers these units:

Core mathematics: C1, C2, C3 & C4
Further Pure mathematics: FP1, FP2 & FP3
Mechanics: M1, M2, M3, M4 & M5
Statistics: S1, S2, S3 & S4
Decision mathematics: D1 & D2

I'm not sure as to the number of possible combinations, but my school offers single maths: C1, C2, C3 & C4, along with either M1 & M2, or S1 & S2 (or, rarely, M1 & S1) depending upon the teacher and other subjects (i.e. those taking subjects such as physics would do mechanics and those taking subjects such as economics would do statistics, but this is not exact) and further maths: C1, C2, C3, C4, FP1, FP2, FP3, M1, M2, M3, S1 & S2 (and possibly S3, I'm not really sure). Anyway, last year I opted for single maths, however, matrices aren't covered until FP1 and FP3, but I wished to study them for their interest and use in mathematics and physics, as well as in order to understand another book, in which some key concepts are explained through matrices. So, I asked my teacher for help and he gave me a quick overview and the FP1 & FP3 textbooks, which I have since been working through - I'm hoping to begin linear transformations in 3-dimensions today, so no doubt I'll have plenty more questions for you . But yes, the eventual answer to your question is that I personally won't be taking an exam at the end (although one could) it is merely an academic curiosity.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Simultaneous equations with 3 unknowns

hi Au101,

academic curiosity

I'm very impressed.  I'd want to take an exam too.

I'd better look up linear transforms.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob