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 if a system of equations has no solution?

Back

The lines representing 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 are the same, meaning they overlap completely.

Front

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

Back

By observing the intersection points of the lines on the graph.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is the slope of a line?

Back

The steepness of the line, calculated as the rise over run.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

What does it mean for two lines to be parallel?

Back

They have the same slope but different y-intercepts.

Front

What does it mean for two lines to be perpendicular?

Back

They intersect at a right angle, and their slopes are negative reciprocals.