Sistem Persamaan Linear Tiga Variabel

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

• x = 0, y = 2, z = 3

• x = 1, y = 1, z = 4

• x = 2, y = 0, z = 1

• x = 3, y = -1, z = 2

Gambarkan grafik dari persamaan 2x + y = 5 dan x - y = 1.

• The graph of the equations 2x + y = 5 and x - y = 1 shows two parallel lines.

• The equations 2x + y = 5 and x - y = 1 intersect at the point (1, 3).

• The graph represents a single line with no intersection points.

• The graph of the equations 2x + y = 5 and x - y = 1 shows two lines intersecting at the point (2, 1).

Gunakan metode substitusi untuk menyelesaikan: x + y + z = 6, 2x - y + z = 3, x + 2y - z = 4.

• x = 2, y = 2, z = 2

• x = 0, y = 0, z = 6

• x = 1, y = 2, z = 3

• x = 17/5, y = 16/5, z = -3/5

Gunakan metode eliminasi untuk menyelesaikan: 3x + 2y + z = 1, 2x - y + 3z = 12, x + y + z = 5.

• x = 1, y = 2, z = 3

• x = -22/3, y = 10/3, z = 8

• x = 0, y = 0, z = 5

• x = -5, y = 5, z = 5

Analisis solusi dari sistem persamaan: x + y + z = 7, 2x + 2y + 2z = 14, x - y + z = 1.

• Infinitely many solutions along the line defined by the equations.

• Only one unique solution is possible.

• No solutions exist for the system.

• The solution is a single point in space.

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

• x = 35/36, y = 1/36, z = 0

• x = 1/2, y = 1/2, z = 1/2

• x = 1, y = 2, z = 3

• x = 0, y = 0, z = 0

Gambarkan grafik dari sistem persamaan: y = 2x + 1, y = -x + 4, dan y = 3.

• The graph of the equations intersects at the point (0, 1).

• The graph of the equations y = 2x + 1, y = -x + 4, and y = 3 intersects at the point (1, 3).

• The graph of the equations is a straight line with a slope of 1.

• The equations have no points of intersection.

Selesaikan sistem persamaan dengan metode substitusi: 5x + 2y + z = 10, x + y + z = 3, 2x - y + 3z = 5.

• x = -1, y = 1, z = 5

• x = 1, y = 2, z = 0

• x = 0, y = 3, z = 0

• x = 2, y = -1, z = -2

Gunakan metode eliminasi untuk menyelesaikan: 2x + 3y + z = 7, 4x - y + 2z = 6, 3x + 2y - z = 4.

• x = 0, y = 2, z = 5

• x = 1, y = 1, z = 1

• x = 2, y = 0, z = 3

• x = 1, y = 2, z = 0

Jelaskan bagaimana perubahan nilai variabel mempengaruhi solusi sistem persamaan: 3x + 4y + 5z = 12, 2x + y - z = 3, x - 3y + 2z = 1.

• Nilai variabel dapat diubah tanpa mempengaruhi persamaan yang ada.

• Setiap perubahan nilai variabel akan mengubah semua solusi menjadi nol.

• Perubahan nilai variabel tidak mempengaruhi solusi sistem persamaan.

• Perubahan nilai variabel mempengaruhi solusi sistem persamaan dengan mengharuskan penyesuaian nilai variabel lainnya agar tetap memenuhi ketiga persamaan.