Graphing Systems of Inequalities and Equations

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables.

Front

What does it mean if a system of inequalities has no solution?

Back

It means that the graphs of the inequalities do not intersect at any point.

Front

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

Back

It means that the graphs of the inequalities overlap completely.

Front

What is the graphical representation of a linear inequality?

Back

A shaded region on one side of a boundary line.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the point into each inequality; if it satisfies all, it is a solution.

Front

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

Back

They have the same slope and will never intersect, resulting in no solutions.

Front

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

Back

They have the same slope and y-intercept, resulting in infinitely many solutions.

Front

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

Back

It represents the unique solution to the system.

Front

How can you graph a system of inequalities?

Back

Graph each inequality as a line, then shade the appropriate region for each.

Front

What is the difference between a solution to an equation and a solution to an inequality?

Back

An equation has specific solutions, while an inequality has a range of solutions.