Types of Solutions from Systems of Equations

Front

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

Back

One Solution, No Solution, Infinitely Many Solutions.

Front

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

Back

The lines intersect at exactly one point.

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 lines coincide, meaning they are the same line.

Front

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

Back

If the equations represent parallel lines.

Front

How can you determine if a system of equations has one solution?

Back

If the equations represent lines that intersect at one point.

Front

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

Back

If the equations represent the same line.

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.