TEST Linear Inequalities & Systems of Inequalities

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What is a linear inequality?

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A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤).

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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 set of a linear inequality represent?

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The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality.

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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.

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How do you find the solution to a system of linear inequalities?

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To find the solution to a system of linear inequalities, graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.

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What does it mean if a system of linear equations has no solution?

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A system of linear equations has no solution if the lines representing the equations are parallel and never intersect.

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What does it mean if a system of linear equations has infinite solutions?

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A system of linear equations has infinite solutions if the equations represent the same line, meaning every point on the line is a solution.

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What is the significance of the point of intersection in a system of linear equations?

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The point of intersection represents the solution to the system, where both equations are satisfied.

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How do you determine if a point is part of the solution set for a linear inequality?

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To determine if a point is part of the solution set, substitute the point's coordinates into the inequality. If the inequality holds true, the point is part of the solution set.

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What is the difference between a solid line and a dashed line when 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 <).