Systems Of Inequalities Word Problems

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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 represent a word problem as a system of inequalities?

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Identify the variables, determine the constraints, and translate the conditions into inequalities.

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What does the symbol '≥' mean in an inequality?

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The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' mean in an inequality?

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The symbol '≤' means 'less than or equal to', indicating that the value on the left is either less than or equal to the value on the right.

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How do you graph a linear inequality?

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1. Graph the corresponding linear equation as a boundary line. 2. Use a solid line for '≤' or '≥' and a dashed line for '<' or '>'. 3. Shade the region that satisfies the inequality.

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What is the feasible region in a system of inequalities?

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The feasible region is the area on the graph where all the shaded regions of the inequalities overlap, representing all possible solutions.

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What is the objective function in a word problem involving inequalities?

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The objective function is the equation that represents the quantity to be maximized or minimized, often related to profit, cost, or resources.

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How do you determine if a point is a solution to a system of inequalities?

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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 a constraint in the context of inequalities?

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A constraint is a condition that limits the values of the variables in a problem, often represented as an inequality.

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What is the significance of the intercepts in a linear inequality?

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Intercepts help identify points where the line crosses the axes, which can be used to graph the inequality and find the feasible region.