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.

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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?

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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.

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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 >).

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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.

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

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

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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.

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What is an ordered pair?

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

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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.