Identify Solutions to 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 that share 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.

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What does the shaded region represent in a graph of inequalities?

Back

The shaded region represents all the possible solutions to the inequality. The common shaded region in a system of inequalities shows the solutions that satisfy all inequalities.

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

Tags

CCSS.HSA.REI.D.12

Front

What does it mean if an ordered pair lies in the unshaded region of a graph?

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If an ordered pair lies in the unshaded region, it means that the pair does not satisfy at least one of the inequalities in the system.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the common shaded region in a system of inequalities?

Back

The common shaded region is where the solutions to all inequalities overlap, representing the set of solutions that satisfy every inequality in the system.

Tags

CCSS.HSA.REI.D.12

Front

How can you graph a system of inequalities?

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To graph a system of inequalities, first graph each inequality separately, using solid or dashed lines as appropriate. Then, identify the common shaded region.

Tags

CCSS.HSA.REI.D.12

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate plane, written in the form (x, y).

Tags

CCSS.HSA.CED.A.3

Front

What does it mean for an ordered pair to be a solution to a system of inequalities?

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An ordered pair is a solution to a system of inequalities if it makes all inequalities in the system true when substituted into them.

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What is the first step in solving a system of inequalities graphically?

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The first step is to graph each inequality on the same coordinate plane.

Tags

CCSS.HSA.REI.D.12