Graphing Systems of three Equations

Front

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

Back

Ordered Triple

Front

A graph of a system of three linear equations in three variables has how many solutions if the lines intersect at a single point?

Back

1

Front

A graph of a system of three linear equations in three variables has how many solutions if the lines are parallel and do not intersect?

Back

0

Front

A graph of a system of three linear equations in three variables has how many solutions if the lines coincide?

Back

Infinitely many solutions

Front

What is the maximum number of solutions a system of three linear equations can have?

Back

3 (one for each variable) or infinitely many if they coincide.

Front

What does it mean if a system of equations has no solution?

Back

The equations represent parallel planes that do not intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same plane or coinciding planes.

Front

In a system of three equations, what does each equation represent geometrically?

Back

Each equation represents a plane in three-dimensional space.

Front

What is the geometric interpretation of a single solution in a system of three equations?

Back

The three planes intersect at a single point.

Front

What is the geometric interpretation of two solutions in a system of three equations?

Back

This scenario is not possible; a system of three equations can have either one, none, or infinitely many solutions.