buat grafik dan cari himpunan penyelesaian sistem persamaan linear berikut: a. 2x + 3y - z = 20 b.3x + 2y + z = 20 c. x + 4y + 2z = 15

Kategori Soal: Matematika - Sistem Persamaan Linear Tiga Variabel
Kelas: X SMA
Pembahasan:

2x + 3y - z = 20
3x + 2y + z = 20
x + 4y + 2z = 15

4x + 6y - 2z = 40
6x + 4y + 2z = 40
_____________ +
10x + 10y = 80

6x + 4y + 2z = 40
x + 4y + 2z = 15
_____________ -
5x + 8y = 25

10x + 10y = 80
5x + 8y = 25

10x + 10y = 80
10x + 16y = 50
___________ -
-6y = 30
y = -5

10x + 10y = 80
10x + 10(5) = 80
10x + 50 = 80
10x = 30
x = 3

2x + 3y - z = 20
2(3) + 3(-5) - z = 2
6 - 15 - z = 2
-z = 11
z = -11

HP = {(3, -5, -11)}