Question

Tentukan himpunan penyelesaian dari sistem persamaan berikut.
x+2y-3z=6
2x-y+4z=2
4x+3y-2z=14

Answer 1

X + 2y - 3z = 6 ~ x + 2y - 3z = 6
2x - y + 4z = 2 ~ 4x + 2y - 8z = 4
-3x + 5z = 2
2x - y + 4z = 2 ~ 6x - 3y + 12z = 6
4x + 3y - 2z = 14 ~ 4x + 3y - 2z = 14
10x + 10z = 20

-3x + 5z = 2 ~ -3x + 5z = 2
x + z = 10 ~ 3x + 3z = 30
8z = 32
z = 4
-3x + 5z = 2 ~ -3x + 5z = 2
x + z = 10 ~ 5x + 5z = 50
-8x = -48
x = 6
4x + 3y - 2z = 14
4(6) + 3y - 2(4) = 14
24 + 3y - 8 = 14
3y + 16 = 14
3y = -2
y = -2/3

jadi,
x = 6
y = -2/6
z = 4