System of Inequalities Review

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What is a system of inequalities?

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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 system of inequalities?

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To graph a system of inequalities, first graph each inequality on the same coordinate plane. Use a dashed line for inequalities with < or >, and a solid line for ≤ or ≥. The solution is the overlapping shaded region.

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What does a dashed line represent in graphing inequalities?

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A dashed line indicates that the points on the line are not included in the solution set, which is the case for inequalities using < or >.

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What does a solid line represent in graphing inequalities?

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A solid line indicates that the points on the line are included in the solution set, which is the case for inequalities using ≤ or ≥.

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What is the solution to a system of inequalities?

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The solution to a system of inequalities is the set of all points that satisfy all inequalities in the system, typically represented by the overlapping shaded region on a graph.

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How can 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 significance of the overlap in shaded regions when graphing inequalities?

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The overlap in shaded regions represents the solution set for the system of inequalities, where all conditions are satisfied.

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What is the difference between a strict inequality and a non-strict inequality?

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A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (≤ or ≥) includes the boundary line.

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How do you identify the correct system of inequalities from a graph?

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To identify the correct system, analyze the slopes and y-intercepts of the lines, and determine whether they are dashed or solid based on the inequalities.

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The graphical representation is a dashed line with a slope of -1/4 and a y-intercept of -3, with the area above the line shaded.