Systems of Inequalities

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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 points that satisfy all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

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How do you graph a system of inequalities?

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To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the appropriate region for each inequality, and the solution set is where the shaded regions overlap.

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 (x, y) that satisfy all inequalities in the system.

Tags

CCSS.HSA.REI.D.12

Front

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

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

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

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What does it mean if a point is not part of the solution set?

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If a point is not part of the solution set, it means that when the coordinates of the point are substituted into the inequalities, at least one inequality is not satisfied.

Tags

CCSS.HSA.REI.D.12

Front

What is the graphical representation of the inequality y < -2x + 5?

Back

The graphical representation is a dashed line for y = -2x + 5, with the area below the line shaded.

Tags

CCSS.HSA.REI.D.12

Front

What is the graphical representation of the inequality y > 2x + 7?

Back

The graphical representation is a dashed line for y = 2x + 7, with the area above the line shaded.

Tags

CCSS.HSA.REI.D.12

Front

How do you find the intersection of two inequalities?

Back

To find the intersection, graph both inequalities and identify the region where the shaded areas overlap. This overlapping region represents the solution set.

Tags

CCSS.HSA.REI.D.12

Front

What is a feasible region in the context of systems of inequalities?

Back

A feasible region is the area on a graph that satisfies all inequalities in a system. It is typically a polygonal shape.

Tags

CCSS.HSA.REI.D.12