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. Rewrite the inequality in slope-intercept form (y = mx + b). 2. Graph the boundary line (dashed for < or >, solid for ≤ or ≥). 3. Shade the region that satisfies the inequality.

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What does the shaded region in a graph of inequalities represent?

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The shaded region represents all the possible solutions to the system of inequalities.

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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 can you determine 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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What does it mean if a point lies outside the shaded region of a graph of inequalities?

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It means that the point is not a solution to the system of inequalities.

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

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The darkest shaded region represents the solution set where all inequalities are satisfied.

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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. 3. This region represents the solution set.

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