Graphing Systems of Inequalities

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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 coordinates of the point 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 an inequality?

Back

A point is a solution to an inequality if it makes the inequality true when the coordinates of the point are substituted into the inequality.

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What is the graphical representation of a linear inequality?

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The graphical representation of a linear inequality is a half-plane, which is the region of the coordinate plane that satisfies the inequality.

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

Back

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

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How do you graph a linear inequality?

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1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for strict inequalities and a solid line for non-strict inequalities. 3. Shade the region that satisfies the inequality.

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What does the solution set of a system of inequalities represent?

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The solution set represents all the points that satisfy all inequalities in the system, often visualized as the overlapping shaded regions on a graph.

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What is the significance of the boundary line in a linear inequality?

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The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not.

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How can you find the intersection of two inequalities?

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

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What is the role of the coefficients in a linear inequality?

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The coefficients determine the slope and position of the boundary line, affecting the orientation and steepness of the line in the graph.