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frx
Group Title
7x+18y=208
18=7(2)+4
7=4(1)+3
4=3(1)+1
GCD(7,18)=1
1=4−3(1)=4−(7−4)=7(−1)+4(2)
7(−1)+(18(2)−7(4))=7(−5)+18(2)
xo=−1040;;yo=416
I know the general solution it a combination of the particular solution and the original equation but I don't understand the different signs, so how do one get the complete solution in general?
 one year ago
 one year ago
frx Group Title
7x+18y=208 18=7(2)+4 7=4(1)+3 4=3(1)+1 GCD(7,18)=1 1=4−3(1)=4−(7−4)=7(−1)+4(2) 7(−1)+(18(2)−7(4))=7(−5)+18(2) xo=−1040;;yo=416 I know the general solution it a combination of the particular solution and the original equation but I don't understand the different signs, so how do one get the complete solution in general?
 one year ago
 one year ago

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Muskan Group TitleBest ResponseYou've already chosen the best response.1
which signs?
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
The answer to this specific equation is xn=1040+18n and yn=4167n and the signs I mean is the pluses and minuses in that solution cause they seem to varie
 one year ago

Muskan Group TitleBest ResponseYou've already chosen the best response.1
  = + + + = + +  =   + = 
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
But how, if the specific solution for x=1040 and the y in the equation is 18 so then the answer is 1040+18n but what if y would have been 18. Is the solution 1040+18n then?
 one year ago

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
once u have a particular solution x0 and y0 for the equation \(ax+by=c\) then the general solution is given by \[ \large x=x_0+\frac{b}{d}t\qquad\text{and}\qquad y=y_0\frac{a}{d}t \] or \[ \large x=x_0\frac{b}{d}t\qquad\text{and}\qquad y=y_0+\frac{a}{d}t \]
 one year ago

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
notice that the signs are apposite. if x has the positive then y has the negative, and vice versa.
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
Thank, really useful! Just to be clear, the first one is ax+by=c and the second is axby=c, right?
 one year ago

frx Group TitleBest ResponseYou've already chosen the best response.0
By the way, whats the d for?
 one year ago

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
d=gcd(a,b) you have two possibilities regarding the sign. i wrote both possibilities.
 one year ago
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