Verifying Solutions Systems of 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 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 verify if a point is a solution to a system of inequalities?

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To verify 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 graphical representation of a system of inequalities?

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The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of each inequality.

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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. It is included in the solution if the inequality is 'greater than or equal to' or 'less than or equal to'.

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What does it mean if a point lies above a boundary line in a system of inequalities?

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If a point lies above a boundary line, it means that the point satisfies the inequality represented by that line.

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What does it mean if a point lies below a boundary line in a system of inequalities?

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If a point lies below a boundary line, it means that the point does not satisfy the inequality represented by that line.

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What is the difference between strict and non-strict inequalities?

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Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) include the boundary line in the solution set.

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How can you determine if a point is a solution to a system of equations?

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Substitute the point's coordinates into each equation. If the point satisfies all equations, it is a solution.

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What is the role of Desmos in verifying solutions to systems of inequalities?

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Desmos is an online graphing tool that allows users to visualize inequalities and check if points are solutions by observing their position relative to the shaded regions.