System of inequalities

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What is a system of inequalities?

Back

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 linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then, shade the region that satisfies the inequality.

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What does the solution to a system of inequalities represent?

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

Front

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

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

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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 significance of the boundary line in a system of inequalities?

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The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not. It helps to identify the solution set.

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What does the inequality y < 2x + 3 represent graphically?

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The inequality y < 2x + 3 represents the region below the line y = 2x + 3, excluding the line itself.

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What is the graphical representation of the inequality x > -3?

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The inequality x > -3 is represented by a vertical dashed line at x = -3, with the region to the right of the line shaded.

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How do you solve a system of inequalities by graphing?

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To solve a system of inequalities by graphing, graph each inequality on the same coordinate plane and identify the overlapping shaded region, which represents the solution.

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

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A feasible region is the area on a graph where all constraints (inequalities) are satisfied. It is typically bounded by the lines representing the inequalities.