Writing Systems of Equations from Word Problems

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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 to the system is the set of values that satisfy all equations simultaneously.

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How do you represent a word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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What does the variable 'x' typically represent in a system of equations?

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In a system of equations, 'x' often represents one of the unknown quantities that need to be determined, such as the number of items or the amount of money.

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What does the variable 'y' typically represent in a system of equations?

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In a system of equations, 'y' often represents another unknown quantity that is related to 'x', such as a different type of item or another amount of money.

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How can you determine the number of solutions in a system of equations?

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A system can have one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (coincident lines).

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What is the importance of defining variables in word problems?

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Defining variables helps clarify what each unknown represents, making it easier to translate the problem into mathematical equations.

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What is the first step in solving a word problem involving a system of equations?

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The first step is to read the problem carefully and identify the key information, including the quantities involved and their relationships.

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How do you check if your solution to a system of equations is correct?

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Substitute the values of the variables back into the original equations to see if they satisfy all equations in the system.

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What is the role of coefficients in a system of equations?

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Coefficients represent the relationship between the variables and the constants in the equations, indicating how much one variable affects another.

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What is a common method for solving systems of equations?

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Common methods include substitution, elimination, and graphing.