Persamaan Tiga Pemboleh Ubah

Selesaikan sistem persamaan berikut: 2x + 3y - z = 7, x - y + 2z = 4, 3x + y + z = 10.

• (0, 0, 0)

• (1, 2, 1)

• (3, 1, 2)

• (2, 1, 3)

Gunakan kaedah penggantian untuk menyelesaikan: x + 2y + 3z = 12, 2x - y + z = 3, x + y - z = 1.

• x = 1, y = 8/5, z = 13/5

• x = 3, y = 1, z = 0

• x = 0, y = 4, z = 2

• x = 2, y = 3, z = 1

Tentukan nilai x, y, dan z bagi sistem persamaan: 4x + y - 2z = 5, 3x + 2y + z = 8, x - y + z = 0.

• x = 0, y = 3, z = 2

• x = 2, y = 1, z = 0

• x = 1, y = 2, z = 1

• x = 1, y = 0, z = 3

Gambarkan graf bagi persamaan: x + y + z = 6, 2x - y + z = 3, x + 3y - z = 4.

• The graph depicts three parallel lines that do not intersect.

• The equations represent a circle in 3D space.

• The graph represents three planes in 3D space, and their intersection point is the solution to the equations.

• The graph shows a single line in 2D space.

Analisis sistem persamaan berikut dan nyatakan sama ada ia konsisten atau tidak: 5x + 2y + z = 10, 3x + 4y + 2z = 20, 2x + y + 3z = 15.

• Dependent

• Consistent

• Inconsistent

• Overdetermined

Selesaikan menggunakan kaedah eliminasi: 3x + 4y + 5z = 12, 2x - 3y + z = 3, x + 2y - z = 1.

• (1, 1, 2)

• (2, 2, 2)

• (0, 0, 0)

• (3, 1, 0)

Tentukan penyelesaian bagi sistem persamaan: 6x + 2y + 3z = 18, 4x + 5y + z = 10, 2x + 3y + 4z = 8.

• x = 2, y = 1, z = 3

• x = 1, y = 2, z = 3

• x = 0, y = 4, z = 2

• x = 3, y = 0, z = 1

Gunakan kaedah penggantian untuk menyelesaikan: 2x + y + z = 5, x - 2y + 3z = 4, 3x + y - z = 7.

• (0, 2, 3)

• (2, 1, 0)

• (1, 1, 1)

• (1.2, 0.8, 1.6)

Gambarkan graf bagi sistem persamaan: x + 2y + z = 9, 2x + y - z = 1, 3x - y + 2z = 6.

• The graph depicts the solution to a quadratic equation.

• The graph represents the intersection of three planes in 3D space.

• The graph represents a circle in 3D space.

• The graph shows a single line in 2D space.

Interpretasi penyelesaian bagi sistem persamaan: 7x + 3y + 2z = 14, 5x + 2y + 4z = 10, 3x + 4y + z = 5.

• x = 2, y = 0, z = 3

• x = 1, y = 2, z = 1

• x = 1, y = 1, z = 2

• x = 0, y = 2, z = 4