jika (x,y) = (2,3) adalah penyelesaian dari sistem persamaan ax + by = 1 dan ay - bx = 8 ,nilai ( 6/11a + 2/11b ) adalah

( x,y ) = ( 2,3 )
ax + by = 1
2a + 3b = 1 ... pers 1
ay - bx = 8
3a - 2b = 8 ... pers 2

pers 1 & 2
2a + 3b = 1 |×2
3a - 2b = 8 |×3
maka
4a + 6b = 2
9a - 6b = 24
------------------(+)
13a = 26
a = 2

subtitusi
2a + 3b = 1
2(2) + 3b = 1
4 + 3b = 1
3b = 1 - 4
3b = - 3
b = - 1

nilai
( 6 / 11a + 2 / 11b )

= 6 / 11(2) + 2 / 11(-1)

= 6/22 - 2/11

= 6/22 - 4/22

= 2/22

= 1/11