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mathmath333
 one year ago
Find the number positive integer solutions of
4x+6y=200
mathmath333
 one year ago
Find the number positive integer solutions of 4x+6y=200

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \color{black}{\begin{align} & \normalsize \text{Find the number positive integer solutions of}\hspace{.33em}\\~\\ & 4x+6y=200 \end{align}}\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1I need to find quick way

Empty
 one year ago
Best ResponseYou've already chosen the best response.1I don't really know but you should look into the Euclidean Algorithm I think that might be a good path to start looking into.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0as this is Diophantine equation i agree with @Empty

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so lets try 2x+3y=100

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6yeah both equations are same but we don't really need euclid algorithm here as finding a particular solution seems kinda easy by inspection. By inspection, (50, 0) is one particular solution

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but Euclid would help in finding general solution to show it's infinite solutions right ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6euclid is for finding particular solution since we already figured that (50, 0) is a particular soltion, we can avoid euclid

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1I found out (50,0),(47,2),.....(2,32) but that took more than 2 min

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6finding "one" particular solution is enough

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0anyway i like this way to show its infinite: dw:1442748565442:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6after you have one particular solution, try finding the "null" solution : 2x + 3y = 0 Easy to see that (3, 2) solves above equation. Therefore the complete solution is given by : `(50, 0) + t(3, 2)`

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6since you want just the positive integer solutions, solve : 50  3t > 0 0 + 2t > 0

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6right, solve it simultaneously you should get an interval of "t" as solution

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0aha i haven't note positive :O

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6I think the answer should be 16

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6nope 0 < t < 16.66 there are exactly 16 positive integers in that interval

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.60 < t < 50/3 leave it like that

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1ok u r right (50,0) doesn't count answer is 16

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6Yep! lets do one more example maybe ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6Find the number of positive integer solutions to the equation 7x + 13y = 700

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6If you prefer, here are the steps : 1) Find any one `particular` solution by inspection 2) Find the `null` solution 3) Write out the complete solution : `particular` + `null`

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1how to find null soln

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6as the name says, it is the solution to the equation 7x + 13y = 0

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6give it a try.. it would feel awesome if you figure out a method to find the null solution on ur own..

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6Very close, but no. plug them in and see if they really produce 0

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6Excellent! that is one null solution. Notice that any multiple of that also works, so all the null solutions are given by ` t(13, 7)` where ` t ` belongs to the set of integers

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6Yes, you have skipped step3 but ok..

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6go ahead find the total count

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1oh this one "3) Write out the complete solution : particular + null"

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6Yes, I was refering to that..

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6Yep! congratulations! Now you know how to solve any linear diophantine equation of form \(ax+by=c\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6so what was your method for finding null solution ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1ax + by = 0 (b,a)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.6that works always! so finding null solution is trivial as you can seethe only hard part is finding a particular solution

anonymous
 one year ago
Best ResponseYou've already chosen the best response.06y=2004x 3y=1002x \[y=\frac{ 1002x }{ 3 }\] by hit and trial when x=2 \[y=\frac{ 1004 }{ 3 }=32\] add successively 3 to the value of x x=2+3=5,y=30 x=5+3=8,y=28 x=11,y=26 .... x=47,y=2 x=50,y=0
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