Jawab:

Penjelasan dengan langkah-langkah:

71x - 48y = -13

d = FPB(71,-48) = 1 => 13 mod 1 = 0  (1 bisa membagi 13)

1) Mencari salah satu solusi (solusi utama):

71 = 48(1) + 23 => 23 = 71(1) - 48(1)

48 = 23(2) + 2 => 2 = 48 - 23(2)

23 = 2(11) + 1 => 1 = 23 - 2(11)

1 = 71(1) - 48(1) + (48-23(2))(-11)

1 = 71(1) - 48(12) - 23(22)

1 = 71(1) - 48(12) + (71(1) - 48(1))(22)

1 = 71(23) - 48(34)

-13 = 2(-6) - 1

-13 = (48-23(2))(-6) - 1

-13 = (48 - 71(2) + 48(2))(-6) - 1

-13 = (71(2) - 48(3))6 - 1

-13 = 71(12) - 48(18) - 71(23) + 48(34)

-13 =  71(-11) - 48(-16)

2) Satu solusi diketahui : x = -11, y = -16

3) Subtitusi : a = x-11, b = y-16

4) Cek apakah 71a - 48b = 0 :

71a - 48b = 71(x+11) - 48(y+16)

= 71x-48y + 71*11 - 48*16

= -13 + 13 = 0

71a = 48b => a = 48n, b = 71n

x = -11+48n, y = -16+71n => solusi umum

(x,y) = (-11+48n, -16+71n)

cek :

71(-11+48n) - 48(-16+71n)

= -(71*11-48*16) + 71*48n - 48*71n

= -13 √