Question

Hitunglah nilai x, y, dan z dari persamaan berikut:
2x + y – 3z = 3
3x + 2y – 4z = 1
X + 4y + z = 15

Answer 1

Eliminate y: (1) dan (2)
2x + y – 3z = 3 | ×2|4x + 2y – 6z = 6
3x + 2y – 4z = 1 | ×1|3x + 2y – 4z = 1 --
x - 2z = 5 ... (4)

(1) dan (3)
2x + y – 3z = 3 | x4 | 8x + 4y – 12z = 12
x + 4y + z = 15 | x1 | x + 4y + z = 15 --
7x - 13z = -3 ...(5)

Eliminasi x: 7×(4) dan (5)
7x - 14z = 35
7x - 13z = -3 --
-z = 38
z = -38

Persamaan (4)
x - 2z = 5 <==> x = 2(-38) + 5
x = -71

Persamaan (1)
2(-71) + y - 3(-38) = 3
y = 3 - 114+142 = 31

Maka x = -71, y = 31, dan z = -38