Systems of Equations and Inequalities Quick Check

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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 point(s) where the equations intersect.

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What does it mean for a point to be a solution to a system of equations?

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A point is a solution to a system of equations if it satisfies all equations in the system.

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What is an inequality?

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An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

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What is the graphical representation of a linear inequality?

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The graphical representation of a linear inequality is a half-plane divided by a line, where one side of the line represents all the solutions.

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How do you determine if a point is a solution to an inequality?

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To determine if a point is a solution to an inequality, substitute the point's coordinates into the inequality. If the inequality holds true, the point is a solution.

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What does the symbol '≥' mean in an inequality?

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The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

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What does the symbol '<' mean in an inequality?

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The symbol '<' means 'less than', indicating that the value on the left is smaller than the value on the right.

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What is the significance of the solution (1, 3) in a system of equations?

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The solution (1, 3) indicates that when x=1 and y=3, both equations in the system are satisfied.

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How can you represent a real-world situation using a system of inequalities?

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A real-world situation can be represented using a system of inequalities by defining variables for the quantities involved and writing inequalities based on the constraints of the situation.

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What is the meaning of 'infinitely many solutions' in a system of equations?

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'Infinitely many solutions' means that there are countless points that satisfy all equations in the system, often occurring when the equations represent the same line.