SOLUTIONS TO 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 that share 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 coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What does it mean if a line is solid in a graph of inequalities?

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A solid line indicates that the points on the line are included in the solution set, meaning the inequality is 'greater than or equal to' (≥) or 'less than or equal to' (≤).

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What does it mean if a line is dotted in a graph of inequalities?

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A dotted line indicates that the points on the line are not included in the solution set, meaning the inequality is 'greater than' (>) or 'less than' (<).

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What is the graphical representation of a solution to a system of inequalities?

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The graphical representation is the shaded region where all inequalities overlap, indicating all possible solutions.

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What is the significance of the intersection of two inequalities?

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The intersection represents the set of points that satisfy both inequalities, which is the solution to the system.

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How can you test if a point is not a solution to a system of inequalities?

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Substitute the point's coordinates into each inequality. If it fails to satisfy any inequality, it is not a solution.

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What is the difference between a solution to an inequality and a solution to an equation?

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A solution to an inequality is a range of values that satisfy the inequality, while a solution to an equation is a specific value that makes the equation true.

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What does the term 'feasible region' refer to in the context of inequalities?

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The feasible region is the area on a graph that represents all possible solutions to a system of inequalities.

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How do you graph a system of inequalities?

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Graph each inequality on the same coordinate plane, using solid or dotted lines as appropriate, and shade the feasible region.