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).

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

Solve the system.

3x - 6y + z = 0

3x - 4y - 4z = 15

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

Solve the system.

x + y + 3z = 20

2x + 4y + 5z = 30

x + y + 4z = 26

Solve the system.

Solve the system

c - 6= 2a + b

- 5b + 5c = 16 +3a

-3a - 6b - c = -24

Solve the system

-4y -2z = 20 + x

-x = 23 + 5y + 5z

x -z = 19 + 3y

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?

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?

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?