Question

Selesaikan himpunan penyelesaian persamaan berikut

3x-2y = 15
5x + 4y = 3
2x - 5z = -44

tolong jawab menggunakan cara

Answer 1

Verified answer

Materi : Persamaan Linear Tiga Variabel (PLTV)
Kelas : X SMA

3x - 2y = 15 ... 1)
5x + 4y = 3 ....2)
2x - 5z = -44 ...3)

Eliminasi nilai y pada pers. 1 dan 2 !

3x - 2y = 15 ... ×2
5x + 4y = 3 .... × 1
◆◆◆◆◆◆◆◆◆◆◆◆◆
6x - 4y =30
5x + 4y = 3
◆◆◆◆◆◆◆◆◆◆◆◆ ( + )
11x = 33
x = 3

Substitusi nilai x ke pers 2 dan 3 , untuk mendapatkan nilai y dan z !

◆> 5x + 4y = 3
◆> 5(3) + 4y = 3
◆> 15 + 4y = 3
◆> 4y = -12
◆> y = -3

◆> 2x - 5z = -44
◆> 2(3) - 5z = -44
◆> 6 - 5z = -44
◆>-5z = -44 - 6
◆> -5z = -50
◆> z = 10

Hp = { 3 , -3 , 10 }

Answer 2

Verified answer

SPLTV

3x - 2y = 15
5x + 4y = 3
2x - 5z = -44

3x - 2y = 15
5x + 4y = 3
----------------
6x - 4y = 30
5x + 4y = 3
_________ +
11x = 33
x = 3

3x - 2y = 15
9 - 2y = 15
-2y = 15 - 9
-2y = 6
y = -3

2x - 5z = -44
6 - 5z = -44
-5z = 6 + 44
-5z = 50
z = 10

HP = {(3, -3, 10)}