How many different solution sets are possible ?

defeated_soldier

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There is an equation ax+by=c , which has solutions that are only positive integers . 'a' and 'b' can take values 1 or 2 . 'c' can take values 1,2 or 3 . How many different solution sets are possible ?

1) 1
2) 2
3)3
4)More than 3


My Solution :

a={1,2}
b={1,2}
c={1,2,3}


so , we can make 2 x 2 x 3 =12 equations . // method of indepency rule


My solution is wrong .

Question :

Q1 . where do you see mistake in my solution ....why its is wrong ?

Q2. what should be the correct approach then ?
 
x+y=1 has no solutions in terms of the given.
x+y=2 has one solution in terms of the given.
x+y=3 has two solutions in terms of the given.
2x+y=3 has one solution in terms of the given.
x+2y=3 has one solution in terms of the given.
 
pka said:
x+y=1 has no solutions in terms of the given.
x+y=2 has one solution in terms of the given.
x+y=3 has two solutions in terms of the given.
2x+y=3 has one solution in terms of the given.
x+2y=3 has one solution in terms of the given.

hi, its not clear.

what is your answer then ?

please explain a bit .
 
You think about it. It is, after all, your problem.
 
why you did not list out these equations ...

2x+2y=1 has no solution.
2x+2y=3 has no solution.


i think these will also be equations ...right ?


From your comment....

x+y=2 has one solution in terms of the given.
x+y=3 has two solutions in terms of the given.
2x+y=3 has one solution in terms of the given.
x+2y=3 has one solution in terms of the given.


Now, i can have x,y as {1,1} ,{1,2},{2,1} , so i can have 3 solution set then .

I think this could be the answer.
 
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