Systems of Equations - Word Problems

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What is a system of equations?

Back

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

Back

Identify the variables, translate the relationships and conditions into equations, and set them equal to each other.

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What does it mean for two companies to charge the same amount?

Back

It means that the total cost equations for both companies are equal, allowing you to find the number of items (e.g., shirts) where their costs match.

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

Back

The first step is to write the equations based on the information given in the problem.

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How do you find the price of each item in a word problem involving costs?

Back

Set up equations based on the total cost and the relationships between the items, then solve the system of equations.

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What does 't = 3n + 8' represent in a word problem?

Back

It represents a relationship where the price of the math textbook (t) is $8 more than three times the price of the novel (n).

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What is the significance of the setup fee in a cost equation?

Back

The setup fee is a fixed cost that must be added to the variable cost per item to find the total cost.

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How can you determine the number of items sold from a total revenue?

Back

By setting up an equation that relates the number of items sold to the total revenue and solving for the variable.

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What does 'x + y = 1550' represent in a football word problem?

Back

It represents the total yards rushed by two players, where x is the yards of one player and y is the yards of the other.

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What is the purpose of using variables in word problems?

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Variables allow us to represent unknown quantities and relationships mathematically, making it easier to solve the problem.