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 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 does it mean for a point to be a solution of an inequality?

Back

A point is a solution of an inequality if it makes the inequality true when the coordinates of the point are substituted into the inequality.

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What is the graphical representation of a linear inequality?

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The graphical representation of a linear inequality is a region of the coordinate plane that is either shaded above or below the line, depending on the inequality sign.

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

Back

'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

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How do you graph the inequality y < 2x + 3?

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To graph y < 2x + 3, first graph the line y = 2x + 3 as a dashed line (not including the line), then shade below the line.

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What is the significance of a dashed line in graphing inequalities?

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A dashed line indicates that points on the line are not included in the solution set of the inequality.

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What is the significance of a solid line in graphing inequalities?

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A solid line indicates that points on the line are included in the solution set of the inequality.

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How do you convert the inequality 3x - 6y > 12 into slope-intercept form?

Back

To convert, rearrange to get y < 1/2x - 2.

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What does the solution set of a system of inequalities represent?

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The solution set represents all the points that satisfy all inequalities in the system, often visualized as a shaded region on a graph.