Systems - One, None, or Infinitely Many

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point, representing a unique solution.

Front

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

Back

The lines are parallel and never intersect.

Front

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

Back

The equations represent the same line, so there are countless points of intersection.

Front

How can you determine if a system of equations has no solution?

Back

If the equations are parallel, they will have the same slope but different y-intercepts.

Front

What is the graphical representation of a system with one solution?

Back

Two lines intersecting at a single point.

Front

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

Back

Two parallel lines that never meet.

Front

What is the graphical representation of a system with infinitely many solutions?

Back

Two overlapping lines that are identical.

Front

If the equations are 2x + 3y = 6 and 4x + 6y = 12, how many solutions does this system have?

Back

Infinitely many solutions.

Front

If the equations are x + 2y = 8 and 10x + 20y = 80, how many solutions does this system have?

Back

Infinitely many solutions.