Question

Tentukan Himpunan Penyelesaian Dari Sistem Persamaan :
x+y+z = -6
x-2y+z = 3
-2x+y+z = 9

Answer 1

X+y+z = -6.....(1)
x-2y+z = 3.....(2)
-2x+y+z = 9...(3)

ambil pers. (1) ubah menjadi ;
x+y+z = -6
z = -6-x-y.... (4)

substitusikan pers. (4) ke pers. (2)
x-2y+z = 3
x-2y+(-6-x-y)= 3
x-2y-6-x-y= 3
-3y=3+6
-3y=9
y=-3

substitusi kan pers. (4) ke pers. (3)
-2x+y+z = 9
-2x+y+(-6-x-y)= 9
-2x+y-6-x-y= 9
-3x=9+6
-3x=15
x=-5

x=-5 , y=-3 substitusikan kepers. (4)

z = -6-(-3)-(-5)
z = 2

HP = {-5,-3,2}