Graphing Systems of Linear Inequalities

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What is a linear inequality?

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A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

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

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A point is a solution to a system of linear inequalities if it satisfies all inequalities in the system simultaneously.

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How do you graph a linear inequality?

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1. Graph the corresponding linear equation as a dashed or solid line. 2. Shade the region that represents the solution set based on the inequality symbol.

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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 points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

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What does shading above a line indicate in graphing inequalities?

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Shading above a line indicates that the solutions are greater than the line's equation (y > mx + b).

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What does shading below a line indicate in graphing inequalities?

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Shading below a line indicates that the solutions are less than the line's equation (y < mx + b).

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What is a system of linear inequalities?

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A system of linear inequalities consists of two or more linear inequalities that are considered together.

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How can you determine if a point is a solution to a system of inequalities?

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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 if a system of linear inequalities has no solution?

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It means that there is no point that satisfies all inequalities in the system, often resulting in parallel lines.

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What does it mean if a system of linear inequalities has infinitely many solutions?

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It means that there are an infinite number of points that satisfy all inequalities, often occurring when the inequalities overlap.