Solving & Graphing Systems of Inequalities

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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 region where the graphs of the inequalities overlap.

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How do you graph a linear inequality?

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1. Graph the corresponding linear equation as a boundary line. 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 the darkest shaded region represent in a graph of inequalities?

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The darkest shaded region represents the solution set of the system of inequalities, where all conditions are satisfied.

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

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The solution set is determined by finding the overlapping region of the shaded areas from each inequality on the graph.

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What does the inequality @@y eq 3@@ represent on a graph?

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It represents all points in the coordinate plane except those where y equals 3, which is a horizontal line.

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What is the significance of the y-intercept in a linear inequality?

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The y-intercept is the point where the line crosses the y-axis, and it helps in graphing the inequality.

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How can you check if a point is a solution to a system of inequalities?

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Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

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