6.4 Writing systems in context

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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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Define variables in a system of equations.

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Variables in a system of equations represent unknown quantities that we aim to solve for, often denoted by letters such as x, y, t, or m.

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What does it mean to solve a system of equations?

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To solve a system of equations means to find the values of the variables that make all equations true at the same time.

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How do you represent the cost of items in a system of equations?

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You can represent the cost of items by defining variables for each item's cost and writing equations based on the total cost.

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What is the first step in writing a system of equations from a word problem?

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The first step is to identify the variables that represent the unknown quantities in the problem.

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How do you write an equation for a total number of items?

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What is the equation for the total cost of items?

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How do you set up a system of equations for a restaurant bill problem?

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Define variables for each type of meal ordered, write an equation for the total number of meals, and another for the total cost.

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

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Coefficients represent the rate or cost associated with each variable in the equations.

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How do you interpret the solution of a system of equations?

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The solution represents the values of the variables that satisfy all equations, indicating the quantities of each item.