Solving Systems- 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 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 are the three main methods for solving systems of equations?

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1. Graphing 2. Substitution 3. Elimination

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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 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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What does it mean if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines that never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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A system has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

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How can 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 word problem involving a system of equations?

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The first step is to define the variables that represent the unknown quantities in the problem.

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In the problem, 'Dennis mowed his neighbor’s lawn for a handful of dimes and nickels, 80 coins in all,' what do the variables represent?

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Let d = number of dimes, n = number of nickels.