Systems: 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 if two lines are parallel in a system of equations?

Back

It means the system has no solution because the lines never intersect.

Front

What does it mean if two lines are the same in a system of equations?

Back

It means the system has infinitely many solutions because every point on the line is a solution.

Front

What does it mean if two lines intersect at one point in a system of equations?

Back

It means the system has one unique solution, which is the point of intersection.

Front

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

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

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

If two lines have the same slope but different y-intercepts, what can you conclude?

Back

The lines are parallel and the system has no solution.

Front

If two lines have different slopes, what can you conclude?

Back

The lines will intersect at one point, meaning the system has one solution.

Front

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

Back

Two overlapping lines on a graph.