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 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 word problem?

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'x' usually represents one of the unknown quantities that you are trying to find.

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What does the variable 'y' typically represent in a word problem?

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'y' usually represents another unknown quantity that is related to 'x' in the context of the problem.

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'x' and 'y' represent the number of two different types of items, with their total being 15.

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

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Coefficients indicate the rate of change or the contribution of each variable to the total. They help define the relationship between the variables.

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How do 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 (same line).

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

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Read the problem carefully to understand the context and identify the variables involved.

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It represents the total monetary value of the bills, where 'x' is the number of $20 bills and 'y' is the number of $50 bills.

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What is the purpose of using two equations in a system?

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Using two equations allows you to find the values of two unknowns by establishing a relationship between them.