System 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 to the system is the set of values that satisfy all equations simultaneously.

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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 reflect the problem's constraints.

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

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It means that the equations represent parallel lines that never intersect, indicating that there are no values for the variables that satisfy all equations.

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

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It means that the equations represent the same line, and any point on that line is a solution to the system.

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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 graphical interpretation of a system of equations?

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The solutions to a system of equations can be represented graphically as the points of intersection of the lines represented by the equations.

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What is a dependent system of equations?

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A dependent system is one where the equations represent the same line, resulting in infinitely many solutions.

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What is an independent system of equations?

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An independent system is one where the equations represent different lines that intersect at exactly one point, resulting in a unique solution.