Precalculus HN: Unit 0 Flashcard 1

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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 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. Then, shade the appropriate region for each inequality. The solution 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, meaning it lies in the shaded region of the graph.

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What is the difference between a solution and a non-solution in a system of inequalities?

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A solution satisfies all inequalities, while a non-solution does not satisfy at least one inequality.

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations in the system.

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How do you solve a system of equations graphically?

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To solve a system of equations graphically, graph each equation on the same coordinate plane. The point(s) where the graphs intersect represent the solution(s) to the system.

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What does it mean if a system of equations has no solution?

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A system of equations has no solution if the graphs of the equations are parallel and never intersect.

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What does it mean if a system of equations has infinite solutions?

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A system of equations has infinite solutions if the equations represent the same line, meaning every point on the line is a solution.

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

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To determine if a point is a solution, substitute the x and y values of the point into each equation. If the equations are satisfied, the point is a solution.

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What is the significance of the solution set in a system of inequalities?

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The solution set represents all possible solutions that satisfy the inequalities, often visualized as a shaded region on a graph.