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What is a system of linear inequalities?

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A system of linear 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 linear 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 part of the solution set.

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What does the graph of a linear inequality represent?

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The graph of a linear inequality represents all the solutions to that inequality, typically shown as a shaded region on one side of the boundary line.

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What is the difference between a solid line and a dashed line in the graph of linear 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 is the solution set of a system of linear inequalities?

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The solution set is the region where the shaded areas of all inequalities overlap on the graph.

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How can you graph a system of linear inequalities?

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1. Graph each inequality as if it were an equation. 2. Use a solid or dashed line as appropriate. 3. Shade the appropriate region for each inequality. 4. Identify the overlapping shaded region.

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What does it mean for a point to be 'not part of the solution set'?

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A point is 'not part of the solution set' if it does not satisfy at least one of the inequalities in the system.

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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 graph into two half-planes, one representing solutions that satisfy the inequality and the other representing those that do not.

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How do you solve a system of linear inequalities by graphing?

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1. Graph each inequality. 2. Identify the feasible region where all inequalities overlap. 3. The overlapping region is the solution set.

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What is an example of a solution to a system of linear inequalities?

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For the inequalities y > 2x + 1 and y < -x + 4, the point (1, 3) is a solution because it satisfies both inequalities.