Graphing Systems of Inequalities

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

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution if it lies in the region where all inequalities overlap on a graph.

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 the inequality y < 2x + 3?

Back

1. Graph the line y = 2x + 3 with a dashed line. 2. Shade below the line to represent y values less than 2x + 3.

Tags

CCSS.HSA.REI.D.12

Front

What does the solution set of a system of inequalities represent?

Back

The solution set represents all the points that satisfy all inequalities in the system, shown as the overlapping shaded region on the graph.

Tags

CCSS.HSA.REI.D.12

Front

How can you identify a point that is NOT a solution to a system of inequalities?

Back

A point that does not satisfy at least one of the inequalities in the system is NOT a solution.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the intersection of two inequalities on a graph?

Back

The intersection represents the set of points that satisfy both inequalities, which is the solution to the system.

Tags

CCSS.HSA.REI.D.12

Front

How do you solve a system of inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Identify the overlapping shaded region, which represents the solution.

Tags

CCSS.HSA.REI.D.12