Systems - Number of 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 representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are the same and overlap at all points.

Front

How can you determine the number of solutions in a system of equations graphically?

Back

By analyzing the intersection points of the lines on a graph.

Front

What is the graphical representation of parallel lines?

Back

Lines that run in the same direction but never meet.

Front

What is the graphical representation of intersecting lines?

Back

Lines that cross each other at one point.

Front

What is the graphical representation of coincident lines?

Back

Lines that lie on top of each other, representing the same equation.

Front

If two lines have the same slope but different y-intercepts, what can be said about their solutions?

Back

They are parallel and have no solutions.

Front

If two lines have different slopes, what can be said about their solutions?

Back

They intersect at one point, meaning there is one solution.