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 graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the region that satisfies the inequality (above or below the line).

Tags

CCSS.HSA.REI.D.12

Front

What does it mean if a point is a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

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

Tags

CCSS.HSA.REI.D.12

Front

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

Back

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

Front

What does the inequality y > 2x - 4 represent graphically?

Back

The inequality y > 2x - 4 represents the region above the line y = 2x - 4, not including the line itself.

Tags

CCSS.HSA.REI.D.12

Front

What is the solution set of a system of inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap.

Tags

CCSS.HSA.REI.D.12

Front

How do you write an inequality from a graph?

Back

To write an inequality from a graph, identify the boundary line and determine if it is dashed or solid, then describe the region (above or below) based on the shading.

Tags

CCSS.HSA.REI.D.12

Front

What does the inequality x < -3 represent?

Back

The inequality x < -3 represents all values of x that are less than -3, which is the region to the left of the vertical line x = -3.

Tags

CCSS.6.EE.B.8

Front

What is the significance of the intersection of two inequalities?

Back

The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously.

Tags

CCSS.HSA.REI.D.12