Solve Systems of Inequalities

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What is a system of inequalities?

Back

A set of two or more inequalities with the same variables. Solutions are the values that satisfy all inequalities in the system.

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How do you graph a system of inequalities?

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1. Graph each inequality as if it were an equation. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the appropriate region for each inequality. 4. The solution is where the shaded regions overlap.

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What does the symbol '≥' mean in an inequality?

Back

'≥' means 'greater than or equal to'. It indicates that the value can be greater than or equal to a certain number.

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What does the symbol '>' mean in an inequality?

Back

'>' means 'greater than'. It indicates that the value must be strictly greater than a certain number.

Front

What does the symbol '≤' mean in an inequality?

Back

'≤' means 'less than or equal to'. It indicates that the value can be less than or equal to a certain number.

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What does the symbol '<' mean in an inequality?

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'<' means 'less than'. It indicates that the value must be strictly less than a certain number.

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

Back

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 inequalities?

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The feasible region is the area on the graph where all the shaded regions overlap, representing all possible solutions to the system.

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What is the significance of the boundary line in an 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 write a system of inequalities from a word problem?

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Identify the constraints and objectives in the problem. Define variables for the unknowns, then translate the constraints into inequalities.