4x-3y+2z=8 3x+2y-4z=9 2x+3y+4z=16

4x - 3y + 2z = 8 ..... (1)
3x + 2y - 4z = 9 ..... (2)
2x + 3y + 4z = 16 .... (3)

Eliminasi (1) dan (2)
4x - 3y + 2z = 8 |.2| 8x - 6y + 4z = 16
3x + 2y - 4z = 9 |.1| 3x + 2y - 4z = 9
---------------------------------------------------- +
................................... 11x - 4y = 25 .... (4)

Eliminasi (2) dan (3)
3x + 2y - 4z = 9
2x + 3y + 4z = 16
------------------------ +
5x + 5y = 25 (bagi 5)
x + y = 5 ............ (5)

Eliminasi (4) dan (5)
11x - 4y = 25 |.1| 11x - 4y = 25
x + y = 5 |kali 4| 4x + 4y = 20
----------------------------------------- +
............................. 15x = 45 => x = 45/15 => x = 3

Substitusi x = 3 ke (5)
x + y = 5
3 + y = 5
y = 5 - 3
y = 2

Substitusi x = 3, y = 2 ke (1)
4x - 3y + 2z = 8
4(3) - 3(2) + 2z = 8
12 - 6 + 2z = 8
6 + 2z = 8
2z = 8 - 6
2z = 2
z = 1

HP = {(3, 2, 1)}

Kelas : X SMA
Pelajaran : Matematika
Kategori : Sistem Persamaan Linear Tiga Variabel
Kata kunci : SPLTV

Penjelasan :

4x - 3y + 2z = 8 .... pers I
3x + 2y - 4z = 9 .... pers II
2x + 3y + 4z = 16 .... pers III

eliminasi z dari pers I dan II

4x - 3y + 2z = 8 |×2|
3x + 2y - 4z = 9 |×1|

8x - 6y + 4z = 16
3x + 2y - 4z = 9
------------------------- +
11x - 4y = 25 ..... pers IV

eliminasi z dari pers II dan III

3x + 2y - 4z = 9
2x + 3y + 4z = 16
------------------------ +
5x + 5y = 25 ..... pers V

eliminasi y dari pers IV dan V

11x - 4y = 25 |×5|
5x + 5y = 25 |×4|

55x - 20y = 125
20x + 20y = 100
---------------------- +
75x = 225
x = 225/75
x = 3

subtitusikan x = 3 ke dalam pers IV

11x - 4y = 25
11(3) - 4y = 25
33 - 4y = 25
-4y = 25 - 33
-4y = -8
y = -8/-4
y = 2

subtitusikan x = 3 dan y = 2 ke dalam pers III

2x + 3y + 4z = 16
2(3) + 3(2) + 4z = 16
6 + 6 + 4z = 16
12 + 4z = 16
4z = 16 - 12
4z = 4
z = 4/4
z = 1

HP = {(3 , 2 , 1)}

semoga membantu