tentukan himpunan penyelesaian dari system persamaan linear tiga variabel berikut 2×-y+2z=9 x-6y-3z=-28 3x+2y+z=16

jawab

2x - y + 2z = 9
x  -6y - 3z = - 28
3x + 2y + z= 16

2x - y + 2z = 9 }kali 3
x - 6y - 3z = -28 }kali 2

6x - 3y + 6z = 27
2x -12y - 6z = - 56 | (+)
8x - 15 y = - 29  (I)

2x - y + 2z = 9
3x + 2y + z = 16}kali 2

2x - y + 2z = 9
6x + 4y + 2z = 32 | (-)
-4x - 5y = - 23 (II)

I dan II
8x - 15 y = - 29
-4x - 5y  = - 23  }kali 2

8x - 15y = - 29
-8x -10y = - 46 | (+)
-25 y = -75
y = 3

8x - 15 y  = - 29
8x - 15(3) = - 29
8x - 45 = - 29
8x = 45 - 29 = 16
x= 2

2x - y + 2z = 9
2(2) - 1(3)+ 2z = 9
4 - 3 + 2z = 9
1 + 2z = 9
2z = 8
z= 4

(x,y,z) = (2, 3, 4)