Solutions to Systems of Inequalities- Graphs!

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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 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 does it mean for a point to be in the overlap of shaded regions?

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A point is in the overlap of shaded regions if it satisfies all inequalities represented by the shaded areas in a graph.

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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 half-plane divided by a line. The line is dashed if the inequality is strict (>, <) and solid if it is inclusive (≥, ≤).

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What is the difference between a strict and non-strict inequality?

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A strict inequality (>, <) does not include the boundary line, while a non-strict inequality (≥, ≤) includes the boundary line.

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How do you solve a system of inequalities by graphing?

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1. Graph each inequality on the same coordinate plane. 2. Identify the overlapping shaded region, which represents the solution set.

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What does the solution set of a system of inequalities represent?

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The solution set represents all possible points (x, y) that satisfy all inequalities in the system.

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How can you check if a point lies in the solution set of a system of inequalities?

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Substitute the point's coordinates into each inequality. If it satisfies all inequalities, it lies in the solution set.

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What is the significance of the shaded region in the graph of inequalities?

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The shaded region indicates all possible solutions that satisfy the inequality. Points in the shaded area are solutions.