Systems of Linear Inequalities

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What is a system of linear inequalities?

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A system of linear inequalities is a set of two or more linear inequalities that involve the same variables. The solution is the set of all points that satisfy all inequalities in the system.

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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 the inequalities in the system, meaning it lies in the region defined by the inequalities.

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What is the difference between a solid line and a dotted line when graphing inequalities?

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A solid line indicates that the points on the line are included in the solution (≥ or ≤), while a dotted line indicates that the points on the line are not included (> or <).

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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 is the graphical representation of a linear inequality?

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The graphical representation of a linear inequality is a shaded region on one side of a line, which shows all the possible solutions to the inequality.

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What does the symbol '>' indicate in an inequality?

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The symbol '>' indicates that the value on the left is greater than the value on the right, and does not include the boundary line.

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What does the symbol '<=' indicate in an inequality?

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The symbol '<=' indicates that the value on the left is less than or equal to the value on the right, including the boundary line.

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How can you tell if a point is above or below a line in a graph?

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A point is above a line if its y-coordinate is greater than the y-value of the line at that x-coordinate, and below if it is less.

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What is the significance of the solution set in a system of inequalities?

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

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What is an example of a system of linear inequalities?

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An example is: y < 2x + 3 and y ≥ -x + 1.