# Assuming something is equal to 1

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

## Answers and Replies

Staff Emeritus
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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

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

u can assume d=1?

Staff Emeritus
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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

Last edited:
hmm i seem to understand number 1)
but 2) i dont 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.

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