Question

Sistem persamaan linear
2x - y = z - 3
x - 2y = z + 2
3x + z = y + 4
mempunyai himpunan penyelesaian {x, y, z} nilai 7x + 7y + 7z adalah....

Answer 1

2x-y = z-3 jadi 2x-y-z =-3....(i)
x-2y = z+2 jadi x-2y-z =2....(ii)
3x+z = y+4 jadi 3x-y+z =4...(iii)

eliminasi pers i dan ii
2x-y-z =-3
x-2y-z =2 -
 3x-y =-1....(iv)
eliminasi pers i dan iii
2x-y-z =-3
3x-y+z =4 +
  5x-y =1....(v)
eliminasi pers iv dan v
3x-y =-1 |5
5x-y =1 |3
15x-5y =-5
15x-6y =3 -
       y =-8
substitusi y=-8 k pers iv
3x-y =-1
3x-(-8) =-1
3x+8 =-1
  3x =-1-8
    x=-3
substitusi y=-8,x=-3 k pers i
2x-y-z =-3
2.-3 - (-8) -z =-3
-6+8-z =-3
2-z =-3
 -z =-3-2
 z =5

7x+7y+7z =7.-3 + 7.-8 + 7.5
               =-21-56+35
               =-42