3a + 2b - c = 3 2a + b - 3c = 4 a - b + 2c = -2 Tentukan nilai a + 10b - 5c = Jawaban saya 42 bener gak ??

Materi : Program Linear
Bahasan : Persamaan Linear 3 Variabel
Metode : Determinan Matriks
Jawaban : 10

Langkah - langkah :
(Terlampir)

Penjelasan singkat :
PLTV ini menggunakan determinan matriks dengan metode sarrus. Diperoleh :
det(D) = -14
det(a) = - 5
det(b) = - 7
det(c) = 13

a = det(a) / det(D)
a = - 5 / - 14
a = 5 / 14

b = det(b) / det(D)
b = - 7 / - 14
b = 1/2

c = det(c) / det(D)
c = 13 / - 14
c = -(13/14)

Sistem Persamaan Tiga Variabel

3a + 2b - c = 3 ...(I)
2a + b - 3c = 4 ...(II)
a - b + 2c = -2 ...(III)

Nilai a + 10b - 5c = ___

============================

Eliminasi Pers. (I) dan (II)
3a + 2b - c = 3 | 1 | 3a + 2b - c = 3
2a + b - 3c = 4 | 2 | 4a + 2b - 6c = 8 -
~~~~~~~~~~~~~~
-a + 5c = -5 ...(IV)

Eliminasi Pers. (II) dan (III)
2a + b - 3c = 4
a - b + 2c = -2 +
~~~~~~~~~~~~~~~
3a - c = 2 ... (V)

Eliminasi Pers. (IV) dan (V)
-a + 5c = -5 | 3 | -3a + 15c = -15
3a - c = 2 | 1 | 3a - c = 2 +
~~~~~~~~~~~~~~~~~
14c = -13
c = -13/14

Substitusi Hasil c ke Pers (V)
3a - c = 2
3a -[-13/14] = 2
3a = 28/14 - 13/14
a = 15/42

Substitusi Hasil c dan a ke Pers (III)
a - b + 2c = -2
15/42 - b + 2[-13/14] = -2
15/42 - b - 78/42 = -84/42
- b - 63/42 = -84/42
- b = -21/42
b = 1/2

Maka didapat Hasil
a = 15/42
b = 21/42
c = - 39/42

Nilai a + 10b - 5c = ___
15/42 + 10[21/42] - 5[-39/42] =
15/42 + 210/42 + 195/42 =
= 420/42
= 10

Maka Jawabannya adalah 10
Semoga Bermanfaat Ya :)