Systems - Number of Solutions

Front

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

Back

The lines are the same and overlap at all points.

Front

What is the solution to the system of linear equations if the point (2,2) is given?

Back

(2,2) is the solution.

Front

What are the possible types of solutions for a system of equations?

Back

No Solution, One Solution, Infinitely Many Solutions.

Front

What does it indicate if two lines in a system are parallel?

Back

They have no solutions because they never intersect.

Front

If a system of equations has one solution, what does that mean graphically?

Back

The lines intersect at exactly one point.

Front

What is the term for a system of equations that has no solutions?

Back

Inconsistent system.

Front

How can you tell if a system of equations has infinitely many solutions?

Back

The equations represent the same line.

Front

What is the graphical representation of a system with no solutions?

Back

Two parallel lines.

Front

If a system of equations has two solutions, what does that imply?

Back

This is not possible for linear equations; they can only have no solution, one solution, or infinitely many solutions.

Front

What is the definition of a consistent system of equations?

Back

A system that has at least one solution.