WU: 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 that share the same variables. The solution is the set of all ordered pairs that satisfy all inequalities in the system.

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How do you graph a system of inequalities?

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To graph a system of inequalities, first graph each inequality as if it were an equation. Use a dashed line for < or > and a solid line for ≤ or ≥. Then, shade the region that satisfies the inequality. The solution to the system is where the shaded regions overlap.

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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 inequalities in the system. This means that when the coordinates of the point are substituted into each inequality, the inequalities hold true.

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

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The shaded region represents all possible solutions to the system of inequalities. Any point within this region is a solution to the system.

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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 the points on the line are included in the solution (≤ or ≥), while a dashed line indicates that the 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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To determine if a point is a solution, substitute the x and y 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 on the boundary line of an inequality?

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If a point lies on the boundary line of an inequality, it may or may not be a solution, depending on whether the inequality is strict (using < or >) or inclusive (using ≤ or ≥).

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What is an ordered pair in the context of inequalities?

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An ordered pair is a pair of numbers (x, y) that represents a point on the Cartesian plane, where x is the horizontal coordinate and y is the vertical coordinate.

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What is the solution set of a system of inequalities?

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The solution set of a system of inequalities is the collection of all ordered pairs that satisfy all inequalities in the system.

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How do you identify a point that is not a solution to a system of inequalities?

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A point that is not a solution will fail to satisfy at least one of the inequalities when its coordinates are substituted into the inequalities.