Systems of Linear Inequalities Practice

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

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How do you graph a linear inequality?

Back

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 linear inequalities represent?

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The solution represents all the points (x, y) that satisfy all inequalities in the system, typically shown as a shaded region on a graph.

Front

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

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> 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 point's coordinates 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 linear inequality?

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The boundary line divides the coordinate plane into two regions: one that satisfies the inequality and one that does not.

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What does the inequality 9x + 25y ≥ 200 represent in a real-world context?

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This inequality represents a constraint where the total earnings from two jobs must be at least $200.

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What does the inequality x + y ≤ 16 represent in a real-world context?

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This inequality represents a constraint on the total number of hours worked at two jobs, which cannot exceed 16 hours.

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How do you find the feasible region for a system of inequalities?

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The feasible region is found by graphing all inequalities and identifying the overlapping shaded area that satisfies all conditions.

Front

What is the role of the x and y intercepts in graphing linear inequalities?

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The x and y intercepts help to plot the boundary line of the inequality and determine where it intersects the axes.