Algebra 2 Section 3.3 Solving Systems of Inequalities

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What is a system of inequalities?

Back

A system of 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 graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line. Then, shade the region that satisfies the inequality (above for 'greater than', below for 'less than').

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What does it mean if a system of inequalities has no solution?

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A system of inequalities has no solution if the shaded regions of the inequalities do not overlap, meaning there are no points that satisfy all inequalities.

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

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A system of inequalities has infinitely many solutions if the shaded regions overlap in a way that creates a continuous area of solutions.

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What is the difference between '>' and '≥' in inequalities?

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'>' means greater than and does not include the boundary line, while '≥' means greater than or equal to and includes the boundary line.

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What is the difference between '<' and '≤' in inequalities?

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'<' means less than and does not include the boundary line, while '≤' means less than or equal to and includes the boundary line.

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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 point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

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What is the graphical representation of the inequality y < 3?

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The graphical representation of y < 3 is a horizontal dashed line at y = 3, with the area below the line shaded.

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What does the solution set of a system of inequalities look like?

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The solution set of a system of inequalities is represented by the overlapping shaded regions of the inequalities on a graph.

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How can you tell if a graph represents a system of inequalities?

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A graph represents a system of inequalities if it shows multiple shaded regions that correspond to different inequalities, with the overlapping area indicating the solution.