Systems of Inequalities (SOI)

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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 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 linear inequality?

Back

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

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What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all inequalities in the system, meaning it lies in the shaded region of the graph.

Front

What is the difference between parallel and perpendicular lines?

Back

Parallel lines have the same slope and never intersect. Perpendicular lines have slopes that are negative reciprocals of each other, meaning their product is -1.

Front

How can you determine if two lines are parallel?

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How do you find the solution set for a system of inequalities?

Back

To find the solution set, graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap. This overlapping region represents the solution set.

Front

What does it mean for a line to be intersecting?

Back

Intersecting lines are lines that cross each other at one point. They have different slopes and will meet at a specific coordinate.

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What is the significance of the point (0,0) in a system of inequalities?

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The point (0,0) is often tested to determine if it is a solution to the system. If it satisfies all inequalities, it is part of the solution set.

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

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To test 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.