Systems of Equations- Real World Problems

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What is a system of equations?

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A set of two or more equations with the same variables that can be solved together.

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What does it mean to solve a system of equations?

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Finding the values of the variables that satisfy all equations in the system simultaneously.

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What is the substitution method in solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is the elimination method in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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How can a system of equations represent a real-world problem?

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By modeling relationships between quantities, such as costs, quantities sold, or other measurable factors.

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What is the meaning of the intersection point of two lines in a graph?

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The point where the two lines meet, representing the solution to the system of equations.

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What is a consistent system of equations?

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A system that has at least one solution.

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What is an inconsistent system of equations?

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A system that has no solutions.

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What is a dependent system of equations?

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A system that has infinitely many solutions, where the equations represent the same line.

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How do you set up a system of equations from a word problem?

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Identify the variables, translate the relationships into equations, and ensure the equations represent the problem accurately.