Answer:
x = 14, y = 18
Explanation:
19x + 47y = 1000
^^^This is a Diophantine equation.
gcd (47,19) = 1
1 is divisible by 1000 -> Euclidean Algorithm.
47=2 (19)+9
19=2 (9)+1 (1 is the gcd )
1=19–2 (9)=19–2 [47–2 (19)=5 (19)-2 (47)
5000 (19)-2000 (47)=1000.
1000 =(5000–47)19 -(2000–19)47
=(5000–106×47)19 - (2000–106×19)47
=18×19-(-14)47
=342 +658
x = 18, y = 14
check: 14 x 47 = 658, 18 x 19 = 342, 658 + 342 = 1000.
