Systems of Equations with Special Solutions

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 no solution?

Back

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

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

The lines represented by the equations are the same line, overlapping completely.

Front

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

Back

If the equations represent parallel lines, they will never intersect.

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 intersecting lines?

Back

Two lines that cross at a single point on a graph.

Front

What is the graphical representation of parallel lines?

Back

Two lines that run alongside each other without ever meeting.

Front

What is the graphical representation of the same line?

Back

Two lines that lie on top of each other, representing the same set of points.

Front

Solve the system: 2x + 3y = 6 and 4x + 6y = 12. What is the solution?

Back

Infinitely Many Solutions.