Math Is Fun Forum

evene

Member

Registered: 2015-10-18

Posts: 272

Homework Problems

I need help solving this system of equation:

t+u=21
u+v=24
v+w=32
w+x=37
x+y=31
y+z=25
z+t=26

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Homework Problems

Hi;

t = 12, u = 9, v = 15, w = 17, x = 20, y = 11, z = 14

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Homework Problems

hi evene,

If you add up everything, you'll get t + u + v + w + x + y + z = 98.

If you add up (t+u) + (v+w) + (x+y) you get 84.

So you can get z.

Similar tricks will allow you to calculate the rest.

Bob

---

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

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Homework Problems

Thanks man!

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Homework Problems

Question: Is there a way to solve this system with elimination, or substitution?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Homework Problems

Sure, that is what I do when I have to do them by hand.

Go down the list and first replace u, then v, then w...

You will end up with this equation

Solving gives t = 12 as above. Now back substitute from the bottom and you will get them all.

There is a honey of a method called Gaussian elimination with partial pivoting that they use for big systems but I think it is best done by a computer. Of course, Gauss claimed he could do it in his sleep but we ain't Gauss. Yeah, I tried it in my sleep just to prove something. Woke up and found that I had drooled all over the equations. No solution was found in the drool though. We liked and used an iterative method called SOR, another fancy name best done by computer.

When tackling a homework problem always know two things, 1) There is a solution and 2) It can be done using simplistic ideas. Here substitution works perfectly and why should it not? It is after all, a homework problem.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Homework Problems

hi evene,

My method did eliminate unknowns so it is a sort of elimination.  I've found it's a trick that often works when you have equations like this.  I call it symmetry although that's just a term I've made up myself.  Each letter occurs the same number of times in similar ways.  It's easy to see when it happens with a set of equations; harder to put into words what it is I'm noticing.  Take two unknowns, say t and u, and swap them over.  The equations are unchanged by this.  That's true for any pair of swaps.  Once I'd noticed that I  though it would be worth adding them all up to get t+u+v+w+x+y+z.  It took a few moments to see how to get a sum with any 6 of them and then it was easy.

Bob

---

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

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Homework Problems

Thanks guys! Really appreciate it.

I'm going to look up the Gauss method thing. Seems interesting!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Homework Problems

Hi;

Just do not try it in your sleep, could get messy.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Homework Problems

Haha... okay!

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Homework Problems

Gaussian Elimination looks very complicated. Wonder how Gauss did it in his sleep.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Homework Problems

He must have slept with one eye open.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: Homework Problems

Or with one side of brain working, like a dolphin.

---

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Homework Problems

Oh god...

Is that even possible? How do dolphins accommodate with half their brain working, and the other side asleep? Sounds like on of those weird but true facts...

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: Homework Problems

I have ever fallen asleep and dreamed with my eyes still open (I was still aware of the surroundings but simultaneously I was experiencing a dream), so dolphins sleep with half their brain didn't really surprise me much.

---

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Homework Problems

I sleep with half my wits and use the other half when awake.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Homework Problems

... ok too much information!

Anyhow, next question:
One morning, each member of Angela's family drank an 8-ounce mixture of coffee with milk. (NASTY!) The amounts of coffee and milk varied from cup to cup, but were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family?

This really seems impossible to me... Also, please provide work because I want to see how you accomplished this fantastic feat!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Homework Problems

Hi;

This is a known problem:

http://artofproblemsolving.com/wiki/ind … Problem_13

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Homework Problems

Thanks!