Systems of Inequalities Practice

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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. Then, shade the region that satisfies the inequality. The solution to the system is where the shaded regions overlap.

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What does it mean if a system of equations has no solution?

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If a system of equations has no solution, it means that the lines representing the equations are parallel and never intersect.

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What does it mean if a system of equations has an infinite number of solutions?

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If a system of equations has an infinite number of solutions, it means that the equations represent the same line, and every point on that line is a solution.

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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 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 the solution to a system of inequalities?

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The graphical representation of the solution to a system of inequalities is the overlapping shaded region of the graphed inequalities.

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What is the difference between a solution and a feasible region in a system of inequalities?

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A solution is a specific point that satisfies all inequalities, while the feasible region is the entire area that contains all possible solutions.

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What does the term 'boundary line' refer to in the context of inequalities?

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A boundary line is the line that represents the equation of an inequality. It divides the coordinate plane into regions that satisfy or do not satisfy the inequality.

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

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A dashed line indicates that the points on the line are not included in the solution set for the inequality (i.e., the inequality is strict, such as < or >).

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

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A solid line indicates that the points on the line are included in the solution set for the inequality (i.e., the inequality is non-strict, such as ≤ or ≥).