Not sure if this a math or physics problem.

[flyingpig]

Homework Statement

My textbook does this A LOT. They divide simultaneous equations to solve. I am taking Linear Algebra right now and such a technique does not exist, then again, all of my equations are linear

Ex. [PLAIN]http://img819.imageshack.us/img819/5299/73710971.png

Find the electric force

My book does it like this

Fx = (1) Tsin(\theta) = F_{e}
Fy = (2) Tcos(\theta) = mg

Divide (1) by (2) = tan(\theta) = \frac{F_{e}}{mg}

Now I have no problem with this, I mean I can see how the mechanics, but I don't understand HOW and WHY this really works (I know this sound ridiculously hypocritical, but my literacy skills are limited). Why don't they use the old substitution method? I personally have never seen this type of method in any of my math class

 

[rock.freak667]

Using substitution would give the same thing, as if you take equation 2 and rewrite it as

T=mg/cosθ and sub this into equation 1, what will you get ?

The division is easier to so since you only have one term on each side and since the T's would cancel out if you divide.

 

[flyingpig]

Using substitution would give the same thing, as if you take equation 2 and rewrite it as

T=mg/cosθ and sub this into equation 1, what will you get ?

The division is easier to so since you only have one term on each side and since the T's would cancel out if you divide.

Does that work if I have linear equations like (made this on top of my head)

4x + 6y = 3

2x+8y=2

 

[SammyS]

Does that work if I have linear equations like (made this on top of my head)

4x + 6y = 3

2x+8y=2

4x = -6y + 3

2x = -8y +2
__________ Dividing gives:

2 = (-6y +3)/(-8y+2)

-16y+4 = -6y +3

1 = 10y

y=1/10

What allows you divide one equation by another?

The equation you divide by states that the RHS is equal to the LHS.

So you're dividing both sides of an equation by the same thing, giving an equivalent equation.

What's the problem with that?

 

[flyingpig]

Doesn't feel natural to me...or just even intuitive. What is this technique called?

 

[cupid.callin]

Nothing ... its simple dividing

 

[cupid.callin]

or even if there is some name, its not at all important.
By dividing you are just skipping a step of rearranging and then substituting!

There no mathematical flaw in that

 

[tiny-tim]

Doesn't feel natural to me...or just even intuitive. What is this technique called?

i think it was mentioned over 2,000 years ago in Euclid's Elements …

if A = B and C = D, then A/B = C/D

 

[flyingpig]

i think it was mentioned over 2,000 years ago in Euclid's Elements …

if A = B and C = D, then A/B = C/D

I will travel back in time and force him to prove it to me.

 

[tiny-tim]

the portal is at your local library