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 with 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 a point is a solution to a system of inequalities?

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To determine if a point is a solution, substitute the x and y values 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?

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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 system of inequalities?

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The graphical representation consists of the shaded regions of the inequalities on a coordinate plane, where the overlapping shaded area represents the solution set.

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

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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 dashed line (for strict inequalities) or solid line (for non-strict inequalities). 2. 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 a shaded region 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 check if a point lies within the solution set of a system of inequalities?

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Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it lies within the solution set.

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What is the role of the origin (0,0) in systems of inequalities?

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The origin can be a solution to a system of inequalities, depending on the specific inequalities. It must be checked by substituting (0,0) into each inequality.