Solving Systems 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 intersect at exactly one point.

Front

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

Back

The lines are parallel and never intersect.

Front

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

Back

The lines coincide, meaning they are the same line.

Front

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

Back

By finding the point where the lines intersect on the graph.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis.

Front

How can you tell if two lines are parallel from their equations?

Back

If they have the same slope but different y-intercepts.

Front

What is the graphical representation of the solution to a system of equations?

Back

The point of intersection of the two lines.

Front

What is the significance of the slopes of two intersecting lines?

Back

The slopes determine the angle of intersection and whether the lines are parallel or not.