Assuming something is equal to 1

[gladius999]

I have always seen people solving equations while assuming something is equal to 1 (usually a constant). Why and under what circumstances can you assume this? what equations are still valid after u assume that it is 1?

Thanks

 

[Office_Shredder]

Post an example, and we can explain why it's a good assumption. Usually you assume a value is equal to 1 because it could be anything (not that you don't know what it is, but that it's arbitrary) and then by assuming it's 1, you can prove that it doesn't satisfy a property for any arbitrary value

 

[gladius999]

a+2b+c=d
2a-b-4c=d
a-c=d

u can assume d=1?

 

[Office_Shredder]

Ok, good example. You actually have to break this up into two cases:
1) d=0. If d=0, you can just solve the equation since there are three equations and three unknowns.

2) d =/= 0. If d is non-zero, divide both sides of every equation by d. Call A=a/d, B=b/d, C=c/d. Then we get A+2B+C=1, 2A-B-4C=1, A-C=1 Then every solution of (A,B,C) corresponds to a set of solutions (Ad,Bd,Cd,d) where d is arbitrary. So we can essentially assume that d=0 or d=1 since we can derive all the solutions from this

 

[gladius999]

hmm i seem to understand number 1)
but 2) i don't get how u can divide both sides of every equation by zero.

another gas example:
P1V=n1RT1
P2V=n1RT2

where V and R are constants

when solving equations can u assume V and R is 1?

 

[maverick_starstrider]

Well R is a constant. It's the gas constant but if in the specific situation you're looking at the volume doesn't change then you can say n1RT1/P1=V and n2RT2/P2=V therefore you can say n1RT1/P1=n2RT2/P2. as for Office Shredder's post when he said "If d is non-zero, divide both sides of every equation by zero" he actually meant "If d is non-zero, divide both sides of every equation by d". I suspect he just had a brain fart and the fingers typed something different then he was thinking.

 

[Office_Shredder]

Yeah, that was just a mistype. I fixed my post to reflect what you should actually do

 

[gladius999]

thnx for ur quick reply guys, i will try apply ur ideas into my thinking:)

 

[HallsofIvy]

You cannot, in general, "assume something is equal to 1". But if you are talking about measured quantitities in physics, you often can assume a system of units so that value is 1 of whatever units you are using. For example, in the standard "meter-seconds" system, the speed of light is 299,792,458 meters per second. But can, just as well take "the distance time travels in one second", one "light second", to be my distance unit rather than the meter. In that case, the speed of light is 1 "light second per second".