systems of equations- how many solutions

Front

What is a system of equations?

Back

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

Front

How many types of solutions can a system of equations have?

Back

Three types: one solution, no solution, or infinitely many solutions.

Front

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

Back

The graphs of the equations intersect at exactly one point.

Front

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

Back

The graphs of the equations are parallel and never intersect.

Front

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

Back

The graphs of the equations are the same line, overlapping each other.

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 no solution?

Back

Two parallel lines that never meet.

Front

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

Back

Two lines that lie on top of each other.

Front

What is the condition for two lines to be parallel?

Back

They have the same slope but different y-intercepts.

Front

What is the condition for two lines to be identical?

Back

They have the same slope and the same y-intercept.