Graphing systems of Inequalities

Front

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 ordered pairs that satisfy all inequalities in the system.

Front

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. Then, shade the appropriate region that satisfies the inequality. The solution set is where the shaded regions overlap.

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What does it mean if a point is a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.

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What is the significance of the boundary line in graphing inequalities?

Back

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

Front

What does the inequality y ≥ x - 3 represent graphically?

Back

It represents the region above or on the line y = x - 3, including the line itself.

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How do you determine if a point is part of the solution set?

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To determine if a point is part of the solution set, substitute the coordinates of the point into each inequality. If all inequalities are satisfied, the point is part of the solution set.

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What does it mean for a point to be outside the solution set?

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A point is outside the solution set if it does not satisfy at least one of the inequalities in the system, meaning it lies outside the shaded region.

Front

What is the difference between a strict and non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (≤ or ≥) includes the boundary line.

Front

How can you tell which region to shade for the inequality y < 2x - 4?

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To determine which region to shade, pick a test point (like (0,0)). If the point satisfies the inequality, shade the region that includes that point.

Front

What does the solution set of a system of inequalities look like?

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The solution set is represented by the overlapping shaded regions of the graphed inequalities.