System Word Problems - Setting Up

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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 point(s) where the equations intersect.

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How do you represent a cost problem with a system of equations?

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You can represent a cost problem by defining variables for the unknowns (e.g., number of items) and writing equations based on the relationships given in the problem.

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What does the slope represent in a linear equation?

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The slope represents the rate of change of the dependent variable with respect to the independent variable. In cost problems, it often represents the cost per item.

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What is the y-intercept in a linear equation?

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The y-intercept is the value of y when x is 0. It represents the fixed cost or starting value in cost problems.

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How do you set up a system of equations for two different pricing models?

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Define variables for the unknowns, write an equation for each pricing model, and set them equal to each other if comparing costs.

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

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The first step is to express both equations in a standard form, usually y = mx + b, where m is the slope and b is the y-intercept.

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

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You can determine the number of solutions by analyzing the slopes of the lines: if they are the same, there are infinitely many solutions; if they intersect, there is one solution; if they are parallel, there are no solutions.

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What is the significance of the fixed cost in a cost equation?

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The fixed cost is the initial amount charged regardless of the quantity purchased, representing costs that do not change with the number of items.

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How do you interpret the solution of a system of equations in a real-world context?

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The solution represents the values of the variables that satisfy all equations in the system, often indicating quantities of items or costs that make two scenarios equal.

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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.