Types of Solutions to System of Equations

Front

What is a system of equations?

Back

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

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means the lines represented by the equations intersect at exactly one point.

Front

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

Back

It means the lines represented by the equations coincide, or are the same line.

Front

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

Back

If the equations are parallel, they will have no points in common.

Front

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

Back

If the equations have different slopes, they will intersect at one point.

Front

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

Back

If the equations are equivalent, they represent the same line.

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 one solution?

Back

Two lines that intersect at a single point.

Front

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

Back

One line that lies on top of another line.