System of Inequalities

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables. Solutions are the set of points that satisfy all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

It means there are no points that satisfy all inequalities simultaneously, often represented by parallel lines that never intersect.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

It means there are countless points that satisfy all inequalities, typically when the inequalities represent the same line or overlapping regions.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the graphical representation of a system of inequalities?

Back

It is represented by shaded regions on a graph, where each region corresponds to the solutions of the inequalities.

Tags

CCSS.HSA.REI.D.12

Front

What does the inequality symbol '≥' indicate?

Back

It indicates that the value on the left is greater than or equal to the value on the right.

Front

What does the inequality symbol '<' indicate?

Back

It indicates that the value on the left is less than the value on the right.

Tags

CCSS.4.NF.A.2

Front

How do you graph the inequality y > 2x - 4?

Back

Graph the line y = 2x - 4 as a dashed line and shade above the line to represent all points where y is greater.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of a dashed line in graphing inequalities?

Back

A dashed line indicates that points on the line are not included in the solution set (for < or > inequalities).

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of a solid line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set (for ≤ or ≥ inequalities).

Tags

CCSS.HSA.REI.D.12