Systems of Equations - Word Problems

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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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What are the methods for solving systems of equations?

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1. Graphing 2. Substitution 3. Elimination 4. Matrix methods

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What does the elimination method involve?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other 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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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 the first step in solving a system of equations word problem?

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Identify the variables and write down the equations based on the information given in the problem.

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If Joe bought 10 cups of coffee and 5 doughnuts for $16.50, how can we express this as an equation?

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10c + 5d = 16.50, where c is the cost of coffee and d is the cost of doughnuts.

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In the problem about Amy and Adam selling cookies, how can we express their sales as equations?

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10s + 2o = 56 (Amy's sales) 9s + 3o = 60 (Adam's sales), where s is the price of sugar cookies and o is the price of oatmeal cookies.

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What does it mean if two equations in a system have the same slope?

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If two equations have the same slope, they are parallel and do not intersect, meaning there is no solution to the system.

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What is the significance of the intersection point of two equations?

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The intersection point represents the solution to the system of equations, indicating the values of the variables that satisfy both equations.