2-5 Solving Systems of Inequalities by Graphing

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What is a system of inequalities?

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

Tags

CCSS.HSA.REI.D.12

Front

How do you determine if an ordered pair is a solution to a system of inequalities?

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To determine if an ordered pair is a solution, substitute the values of the ordered pair into each inequality. If the pair satisfies all inequalities, it is a solution.

Front

What does it mean to graph an inequality?

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Graphing an inequality involves representing the solutions of the inequality on a coordinate plane, showing the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

Front

What type of line is used when graphing inequalities with ≤ or ≥?

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A solid line is used when graphing inequalities with ≤ (less than or equal to) or ≥ (greater than or equal to) to indicate that points on the line are included in the solution.

Tags

CCSS.HSA.REI.D.12

Front

What type of line is used when graphing inequalities with < or >?

Back

A dashed line is used when graphing inequalities with < (less than) or > (greater than) to indicate that points on the line are not included in the solution.

Tags

CCSS.HSA.REI.D.12

Front

What is the solution set of a system of inequalities?

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The solution set is the region on the graph where the shaded areas of all inequalities overlap, representing all ordered pairs that satisfy all inequalities.

Tags

CCSS.HSA.REI.D.12

Front

How do you find the boundary line of an inequality?

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To find the boundary line of an inequality, rewrite the inequality as an equation (e.g., y = mx + b) and graph that line.

Tags

CCSS.HSA.REI.D.12

Front

What does it mean if a point lies on the boundary line of an inequality?

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If a point lies on the boundary line of an inequality with ≤ or ≥, it is included in the solution set. If it lies on the line of < or >, it is not included.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the shaded region in the graph of an inequality?

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The shaded region represents all the solutions to the inequality, indicating which points satisfy the inequality.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

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