Solving Systems of Equations by Graphing

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have one solution?

Back

The graphs of the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

The graphs of the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

The graphs of the equations are the same line, meaning they intersect at every point on the line.

Front

How do you determine the solution of a system of equations by graphing?

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What is the graphical representation of intersecting lines?

Back

Two lines that cross at a single point, indicating one solution.

Front

What is the graphical representation of parallel lines?

Back

Two lines that run alongside each other without ever meeting, indicating no solution.

Front

What is the graphical representation of the same line?

Back

A single line that represents both equations, indicating infinitely many solutions.

Front

How can you verify if a point is a solution to a system of equations?

Back

By substituting the point's coordinates into both equations to see if they hold true.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, satisfying all equations involved.