Graph Systems of Linear Inequalities

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What is a system of linear inequalities?

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A system of linear inequalities is a set of two or more inequalities that involve the same variables. The solution is the set of all points that satisfy all inequalities in the system.

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

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A point is a solution to a system of inequalities if it satisfies all the inequalities in the system, meaning it lies in the region defined by the inequalities on a 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 coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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What is the graphical representation of a linear inequality?

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The graphical representation of a linear inequality is a shaded region on a coordinate plane, where the boundary line represents the equation of the inequality.

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What does the symbol '>' indicate in an inequality?

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'>' indicates that the value on the left is greater than the value on the right, and the boundary line is not included in the solution set.

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What does the symbol '≥' indicate in an inequality?

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'≥' indicates that the value on the left is greater than or equal to the value on the right, and the boundary line is included in the solution set.

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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 coordinate plane into two regions: one that satisfies the inequality and one that does not.

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How do you graph a linear inequality in two variables?

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1. Graph the boundary line as if it were an equation. 2. Use a dashed line for '>' or '<' and a solid line for '≥' or '≤'. 3. Shade the region that satisfies the inequality.

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

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A system of inequalities has no solution if the shaded regions of the inequalities do not overlap, meaning there are no points that satisfy all inequalities.

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What does it mean if a system of inequalities has infinitely many solutions?

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A system of inequalities has infinitely many solutions if the shaded regions overlap in such a way that there are countless points that satisfy all inequalities.