#Linear equations

54 messages · Page 1 of 1 (latest)

undone folio
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Hey..
this might seem like a stupid question:
Find the number of solutions for the linear equation q - 49 = 2p where p and q are natural numbers and p<=q.
now, i thought there were infinite solutions, however my book says it's 16..
am i missing something?

exotic aspenBOT
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wraith crag
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no way bro

undone folio
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what

wraith crag
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doesnt a linear euqn in 2 variables have infinite solutions

undone folio
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thats what i thought

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but the book says 16

wraith crag
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ok so lets see if p=q then its only 1 solution

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now if p<q

undone folio
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any odd number 51 and above works for q

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so is the book wrong

wraith crag
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why doesnt 50 work

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it also worms

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u can use any no.

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like if p = lets say 1

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then q just has to be more than 1

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so

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ahh

undone folio
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but p has to be natural

wraith crag
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ahh ok i get it

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yeah 1 is natural

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q will always be larger bro

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cuz its - 49

undone folio
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yea

wraith crag
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when it goes over rhs it automatically adds up to 2p and 2p itself is larger than p

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so it should be infinite

undone folio
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dude the thing is

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its an olympiad book

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and this question appeared in a previous years' olympiad question papers

wraith crag
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what was the answer

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16?!?

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ro take natural no. there will be no case where p is larger than q

undone folio
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yea

wraith crag
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is ur question correct?

undone folio
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yea

wraith crag
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bro it has to be infinite

undone folio
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imo there was probably a limit or something like p<20 and they forgot to include that

wraith crag
undone folio
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thanks tho anyway

wraith crag
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well if the question is as u asked then its infinite

undone folio
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yea

serene badge
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nope there is a limit

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lol

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p <= q

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hmmm

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oh wait

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that never happens

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bru

wraith crag
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q is always bigger einstein

serene badge
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yeah something is weird in this question

wraith crag
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ye