Agar sistem persamaan di bawah ini bernilai benar :

12x + 17y = 53 (×17)
17x + 12y = 63 (×12)

204x + 289y = 901
204x + 144y = 756
(dikuragi)
145y = 145
y = 145/145
y = 1

12x + 17y = 53
12x + 17(1) = 53
12x = 53-17
12x = 36
x = 36/12
x = 3

penyelesaian =
x = 3
y = 1

12x + 17y = 53 dikali 17
17x + 12y = 63 dikali 12

204x + 289y = 901
204x + 144y = 756
________________-
145y = 145
y = 145/145
y = 1

12x + 17y = 53 dikali 12
17x + 12y = 63 dikali 17

144x + 204y = 636
289x + 204y = 1071
________________-
-145x = -435
x = -435/-145
x = 3

(x,y) (3,1)