Graphing systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

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

Back

A system of inequalities has no solution if the shaded regions of the inequalities do not overlap, meaning there are no points that satisfy all inequalities.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

A system of inequalities has infinitely many solutions if the shaded regions overlap in such a way that there are an infinite number of points that satisfy all inequalities.

Tags

CCSS.HSA.REI.D.12

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a half-plane, which is the area above or below the line, depending on the inequality sign.

Tags

CCSS.HSA.REI.D.12

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Tags

CCSS.HSA.REI.D.12

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane, shade the appropriate region for each, and identify the overlapping shaded area.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the shaded region in a graph of inequalities?

Back

The shaded region represents all possible solutions to the inequality. Any point within this region satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean for two inequalities to be parallel?

Back

Two inequalities are parallel if their corresponding lines have the same slope but different y-intercepts, meaning they will never intersect.

Tags

CCSS.HSA.REI.D.12

Front

Can a system of parallel inequalities have a solution?

Back

Yes, a system of parallel inequalities can have a solution if the inequalities are not strict (i.e., they include equalities), allowing for overlapping shaded regions.

Tags

CCSS.HSA.REI.D.12