Three Variable Systems

The solution of a system of three linear equations in three variables, x,y, and z, is called a(n) ___________________ (x,y,z).

• Ordered Pair

• Integer

• Ordered Triple

• Sum

What is your solution if your variables go away and you are left with 0 = 0?

• No Solution

• All Real Numbers

• Infinitely Many Solutions

• (x, y, z)

Solve the system.

3x - 6y + z = 0

3x - 4y - 4z = 15

-6x + 8y + 9z = -33

Evaluate responses using AI:

OFF

Solve the system.

x + y + 3z = 20

2x + 4y + 5z = 30

x + y + 4z = 26

Evaluate responses using AI:

OFF

Solve the system.

x - 2y + z = 33
y + 2z = 5
z = 4

Evaluate responses using AI:

OFF

Solve the system

c - 6= 2a + b

- 5b + 5c = 16 +3a

-3a - 6b - c = -24

• (-2, 4, 6)

• Infinitely Many Solutions

• (-8, -12, 5)

• No Solution

Solve the system

-4y -2z = 20 + x

-x = 23 + 5y + 5z

x -z = 19 + 3y

• (2, -6, 1)

• (1, -4, 5)

• (-1, -12, -8)

• (0, -8, -6)

Each image contains three planes which represent possible solution types for a 3x3 system of linear equation. Which image(s) represents a 3x3 system of linear equations with one solution?

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Each image contains three planes which represent possible solution types for a 3x3 system of linear equation. Which image(s) represents a 3x3 system of linear equations with infinite solutions?

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Each image contains three planes which represent possible solution types for a 3x3 system of linear equation. Which image(s) represents a 3x3 system of linear equations with no solution?

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