Systems of Equations and Inequalities (Graphs) #2

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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.

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

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

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

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What is the graphical representation of a system of inequalities?

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The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to an inequality. The solution set is where the shaded regions overlap.

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What is the significance of the boundary line in a system of inequalities?

Back

The boundary line represents the points where the inequality changes from true to false. If the inequality is strict (e.g., < or >), the line is dashed; if it is inclusive (e.g., ≤ or ≥), the line is solid.

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What does it mean if a point is above a boundary line in a graph of an inequality?

Back

If a point is above the boundary line of an inequality of the form y < mx + b, it means that the point satisfies the inequality.

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What does it mean if a point is below a boundary line in a graph of an inequality?

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If a point is below the boundary line of an inequality of the form y > mx + b, it means that the point satisfies the inequality.

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How can you identify a solution point from a list of options?

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Substitute each point into the inequalities of the system. The points that satisfy all inequalities are the solution points.

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What is the difference between a solution point and a non-solution point?

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A solution point satisfies all inequalities in the system, while a non-solution point does not satisfy at least one inequality.

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What is an example of a solution point for a system of inequalities?

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For example, if the system is y < 2x + 1 and y > -x - 2, the point (0,0) is a solution point.