Writing Systems of Equations from 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 set of values that satisfy all equations in the system.

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How do you represent a word problem as a system of equations?

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Identify the variables, write equations based on the relationships described in the problem, and ensure the equations reflect the conditions given.

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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 make all equations true simultaneously.

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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.

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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 remaining variable.

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How can you check if your solution to a system of equations is correct?

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Substitute the values of the variables back into the original equations to see if they satisfy all equations.

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

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Coefficients represent the relationship between the variables in the equations. They determine how changes in one variable affect the other.

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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, meaning there are no values that satisfy both equations.

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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 every point on the line is a solution.

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How do you write an equation for a total cost problem?

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Identify the cost per item and the number of items, then write an equation that represents the total cost as the sum of the costs of each item.