Systems of Linear Inequalities Practice Test

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What is a linear inequality?

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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 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 linear inequalities?

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A point is a solution to a system of linear inequalities if it lies in the shaded region of the graph representing all inequalities in the system.

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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 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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What is the solution set of a system of linear inequalities?

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The solution set is the set of all points that satisfy all inequalities in the system, represented by the overlapping shaded regions on the graph.

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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 separates the graph into two regions: one that satisfies the inequality and one that does not. It is crucial for determining the solution set.

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What is a system of linear inequalities?

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A system of linear inequalities consists of two or more linear inequalities that are considered together. The solution is the intersection of the solution sets of each inequality.

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How do you find the intersection of two linear inequalities?

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To find the intersection, graph both inequalities and identify the region where their shaded areas overlap. This overlapping region represents the solution to the system.