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?

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

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What is the formula for calculating total cost with a setup fee?

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Total Cost = (Cost per item * Number of items) + Setup fee.

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How do you set up an equation from a word problem involving coins?

Back

Define variables for each type of coin, create an equation for the total number of coins, and another for the total value.

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

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Coefficients represent the rate of change or the cost per item in a word problem, indicating how much each variable contributes to the total.

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How can you determine the number of items sold from a system of equations?

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By solving the system of equations simultaneously, you can find the values of the variables that satisfy both equations.

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What does it mean to solve a system of equations graphically?

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It means to plot the equations on a graph and find the point(s) where they intersect, which represents the solution.

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What is the elimination method in solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.