Systems of Linear Inequalities (A1.1.3.2.1, A1.1.3.2.2) FL

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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 linear inequalities that share the same variables. The solution is the region where the graphs of the inequalities overlap.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then shade the region that satisfies the inequality.

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What does the symbol '<' indicate in a linear inequality?

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The symbol '<' indicates that the values of the variable are less than the value on the other side of the inequality.

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What does the symbol '>' indicate in a linear inequality?

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The symbol '>' indicates that the values of the variable are greater than the value on the other side of the inequality.

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What does the symbol '≤' indicate in a linear inequality?

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The symbol '≤' indicates that the values of the variable are less than or equal to the value on the other side of the inequality.

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What does the symbol '≥' indicate in a linear inequality?

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The symbol '≥' indicates that the values of the variable are greater than or equal to the value on the other side of the inequality.

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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 is the feasible region in a system of linear inequalities?

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The feasible region is the area on the graph where all the inequalities overlap. It represents all possible solutions to 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 regions: one that satisfies the inequality and one that does not. The line itself is included if the inequality is ≤ or ≥.

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How can you express a real-world situation as a system of linear inequalities?

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Identify the constraints in the situation (like budget, quantity, etc.) and express them as inequalities using variables to represent the quantities involved.