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Question Number 42291 by Joel578 last updated on 22/Aug/18

y = ((1080 − 19x)/(49)) (x,y ∈ Z) Find (x,y)

y=1080−19x49(x,y∈Z)Find(x,y)

Answered by ajfour last updated on 22/Aug/18

19x+49y=1080 19(x+y)+30y=30×36 x+y = 30n (n∈Z ) ⇒19n +y = 36 ⇒ n=1, y=17 , x=13 . also if n=2 , y=−2, x=62 if n=3, y=−21 , x=111 if n=−1 , y=55 , x= −85 and so on..

19x+49y=108019(x+y)+30y=30×36x+y=30n(n∈Z)⇒19n+y=36⇒n=1,y=17,x=13.alsoifn=2,y=−2,x=62ifn=3,y=−21,x=111ifn=−1,y=55,x=−85andsoon..

Commented by Joel578 last updated on 22/Aug/18

thank you very much

thankyouverymuch

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