3.5 Linear Systems in Three Variables_enrichment

Front

What is the solution of a system of three linear equations in three variables called?

Back

Ordered Triple (x, y, z)

Front

What is the value of y in the system if y = 3?

Back

y = 3

Front

What does it mean if you simplify a system and are left with 0 = 0?

Back

Infinitely Many Solutions

Front

What does it mean if you simplify a system and are left with 0 = -8?

Back

No Solution

Front

What is the general form of a linear equation in three variables?

Back

Ax + By + Cz = D, where A, B, C, and D are constants.

Front

What is the graphical representation of a system of three linear equations?

Back

The intersection of three planes in three-dimensional space.

Front

What is the significance of an ordered triple in the context of linear systems?

Back

It represents the unique solution to the system of equations.

Front

What is the condition for a system of equations to have no solution?

Back

The equations represent parallel planes that do not intersect.

Front

What is the condition for a system of equations to have infinitely many solutions?

Back

The equations represent the same plane or coincide.

Front

How can you determine if a system of equations is consistent or inconsistent?

Back

By analyzing the relationships between the equations and their graphical representations.