Front

What is a system of inequalities?

Back

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 as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the appropriate region for each inequality, and the solution 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, meaning it lies in the overlapping shaded region of the graph.

Front

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 x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What is the difference between a solid line and a dashed line in graphing inequalities?

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

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What does the inequality y > 2x - 4 represent graphically?

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The inequality y > 2x - 4 represents the region above the line y = 2x - 4, where all points (x, y) satisfy the inequality.

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What does the inequality y ≤ x + 4 represent graphically?

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The inequality y ≤ x + 4 represents the region below and including the line y = x + 4, where all points (x, y) satisfy the inequality.

Front

How do you find the intersection of two inequalities?

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To find the intersection of two inequalities, graph both inequalities and identify the region where the shaded areas overlap. This overlapping region represents the solution set.

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What is a feasible region in the context of systems of inequalities?

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A feasible region is the area on a graph that satisfies all inequalities in a system. It is typically a polygonal shape formed by the intersection of the inequalities.

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What is the significance of the vertices of the feasible region?

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The vertices of the feasible region are important because they represent potential solutions to the system of inequalities, often used in optimization problems.