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 a system of equations has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The lines intersect at exactly one point.

Front

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

Back

The lines represented by the equations are the same line.

Front

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

Back

By graphing the equations and observing the intersection points.

Front

What are parallel lines in the context of systems of equations?

Back

Lines that have the same slope but different y-intercepts, indicating no solutions.

Front

What are intersecting lines in the context of systems of equations?

Back

Lines that cross at one point, indicating one unique solution.

Front

What are coincident lines in the context of systems of equations?

Back

Lines that lie on top of each other, indicating infinitely many solutions.

Front

What is the graphical representation of a system of equations?

Back

A graph showing the lines of the equations, where their intersections represent the solutions.

Front

What is the slope of a line?

Back

The steepness of the line, calculated as the rise over run (change in y over change in x).