Question

Tentukan himpunan penyelesaian dari persamaan x+y+z=-1 , x+2y+3z=5 , dan 3y-2y-z=-9

Answer 1

Verified answer

x + y + z = -1..............(1)
x + 2y + 3z = 5..........(2)
3x - 2y - z = -9............(3)

dari (1) dan (2)
x + y + z = -1
x + 2y + 3z = 5
---------------------- (-)
  y + 2z = 6 ...............(4)

dari (1) dan (3)
3x + 3y + 3z = -3
3x - 2y - z = -9
--------------------- (-)
   5y + 4z = 6..............(5)

dari (4) dan (5)
2y + 4z = 12
5y + 4z = 6
----------------- (-)
3y = -6
y = -2

subtitusi
y + 2z = 6
-2 + 2z = 6
2z = 6 + 2
2z = 8
z = 4

subtitusi
x + y + z = -1
x + (-2) + (4) = -1
x + 2 = -1
x = -3

jadi HP = {(-3 , -2 , 4)}

Answer 2

X+y+z = -1
x+2y+3z= 5 (dikurangi) = -y - 2z = -6

x+y+z. = -1. |×3| 3x+3y+3z= -3
3y-2y-z = -9 |×1| 3y-2y-z. = -9. (dikurangi)
= 5y+4z. = 6

maka -y-2z=-6|×2| -2y-4z = -12
5y+4z=6|×1| 5y+4z.= 6. (ditambah)
3y. = -6
y. = -6/3 = -2
substitusikan 5y+4z = 6
5(-2)+4z=6
-10 +4z=6
4z =6+10=16
z. = 16/4=4
x+y+z = -1
x+(-2)+4=-1
x+2. =-1
x. =-1-2=-3

jadi x=-3,y=(-2),dan z=4

semoga membantu.. .