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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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 satisfy all equations in the system simultaneously.

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What is the elimination method?

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

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What is the substitution method?

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

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What is the graphing method?

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The graphing method involves graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

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What is a word problem in the context of systems of equations?

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A word problem is a mathematical problem that is presented in a narrative form, requiring the formulation of equations based on the given information.

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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 represent the same scenario.

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What is a setup fee in a pricing problem?

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A setup fee is a fixed charge that is added to the total cost, regardless of the quantity purchased.

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How can you determine when two companies charge the same amount?

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Set the equations representing the total costs of each company equal to each other and solve for the variable representing quantity.

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What does it mean for one quantity to be '4 times as many' as another?

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If one quantity is '4 times as many' as another, it can be expressed as y = 4x, where y is the larger quantity and x is the smaller quantity.