Solving system of equation 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 described in the problem into equations, and ensure the equations reflect the problem's constraints.

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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 in the system true.

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What are the common methods for solving systems of equations?

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The common methods include substitution, elimination, and graphing.

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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 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 a word problem?

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A word problem is a mathematical problem that is presented in a narrative form, requiring interpretation and translation into mathematical expressions.

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

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You can check the solution by substituting the values back into the original equations to see if they hold true.

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What is a linear equation?

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A linear equation is an equation that represents a straight line when graphed, typically in the form ax + by = c, where a, b, and c are constants.

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

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The coefficients represent the relationship between the variables in the equations, indicating how much one variable changes in relation to another.