Solving 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 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 graph a system of inequalities?

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To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the region that satisfies the inequality. The solution set is where the shaded regions overlap.

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What does it mean for a point to be a solution to a system of inequalities?

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A point is a solution to a system of inequalities if it satisfies all inequalities in the system. This means that when the coordinates of the point are substituted into each inequality, the inequalities hold true.

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What is the significance of the boundary line in a system of inequalities?

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The boundary line represents the points where the inequality changes from true to false. Points on the line may or may not be included in the solution set, depending on whether the inequality is strict (< or >) or inclusive (≤ or ≥).

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How do you determine if a point is a solution to a given inequality?

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To determine if a point is a solution to an inequality, substitute the x and y values of the point into the inequality. If the resulting statement is true, then the point is a solution.

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What is the meaning of the inequality 2x + 3y ≥ 20?

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This inequality means that the combination of 2 times the x-value and 3 times the y-value must be greater than or equal to 20. It represents a region in the coordinate plane.

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What does the inequality x + y < 10 represent in a real-world context?

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This inequality could represent a situation where the total number of items (x and y) must be less than 10, such as the number of shots taken in a basketball game.

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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 points, while a non-strict inequality (≤ or ≥) includes the boundary points in the solution set.

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How can you write a system of inequalities from a word problem?

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To write a system of inequalities from a word problem, identify the variables, determine the constraints (conditions) given in the problem, and express these conditions as inequalities.

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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 typically represented as a shaded region on a graph, where all points in the region satisfy all inequalities in the system.