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 lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations are the same line, overlapping completely.

Front

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

Back

The (x,y) coordinates must satisfy both equations.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane.

Front

What is the solution to a system of equations?

Back

The point or points where the lines intersect.

Front

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

Back

It represents the values of the variables that satisfy all equations in the system.

Front

What happens to the solution if the lines of a system of equations are parallel?

Back

There is no solution because the lines do not intersect.

Front

What is the relationship between the slopes of two lines that are the same?

Back

They have identical slopes.