Notes for Solving Systems (Inequalities) with Desmos

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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 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 satisfy an inequality?

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A point satisfies an inequality if, when its coordinates are substituted into the inequality, the resulting statement is true.

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What is the difference between '<' and '≤' in inequalities?

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The symbol '<' indicates that the value is strictly less than, while '≤' indicates that the value can be less than or equal to.

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What is the significance of the boundary line in a system of inequalities?

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The boundary line represents the points where the inequality changes from true to false. For '<' or '>', the line is dashed; for '≤' or '≥', the line is solid.

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How do you graph a system of inequalities?

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1. Graph each inequality as a line. 2. Use a dashed line for '<' or '>' and a solid line for '≤' or '≥'. 3. Shade the appropriate region that satisfies the inequality.

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What does it mean if a point lies in the shaded region of a graph of inequalities?

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If a point lies in the shaded region, it means that the point satisfies all inequalities in the system.

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What is the solution set of a system of inequalities?

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The solution set is the collection of all points that satisfy all inequalities in the system, often represented as a shaded region on a graph.

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

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What is the role of Desmos in solving systems of inequalities?

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Desmos is an online graphing calculator that allows users to graph inequalities and visualize the solution set easily.