Question

Tentukan himpunan pemyelesaian system persamaan linear dibawah ini
4x + 2y - 2z= 3, 2x + 2y + 2z=8, 2x - 4y + 2z=2
Tolong yaaaaa

Answer 1

Verified answer

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

(1) + (2)
4x + 2y - 2z = 3
2x + 2y + 2z = 8
----------------------- +
6x + 4y = 11 .... (4)

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

(4) - (5)
6x + 4y = 11
6x - 2y = 5
----------------- -
..... 6y = 6 => y = 1

6x + 4y = 11 => 6x + 4(1) = 11 => 6x = 7 => x = 7/6

2x + 2y + 2z = 8
x + y + z = 4
z = 4 - y - x = 4 - 1 - 7/6 = 11/6

HP = {(7/6, 1, 11/6)}

Answer 2

Verified answer

Sistem Persamaan Linear Tiga Variabel.
Kelompok wajib kelas X kurikulum 2013 revisi 2016.

4x + 2y - 2z = 3
2x + 2y + 2z = 8 → x + y + z = 4
2x - 4y + 2z = 2 → x - 2y + z = 1

x + y + z = 4
x - 2y + z = 1
----------------- -
3y = 3 → y = 1

4x + 2y - 2z = 3
2x + 2y + 2z = 8
---------------------- -
2x - 4z = -5

4x + 2y - 2z = 3
x - 2y + z = 1
--------------------- +
5x - z = 4

2x - 4z = -5 | x1 | 2x - 4z = -5
5x - z = 4    | x4 | 20x - 4z = 16
                           ------------------ -
                            -18x = -21 → x = 7/6
5(7/6) - z = 4 → z = 11/6

HP = {(7/6, 1, 11/6)}