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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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 context.

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What does it mean to solve a system of equations?

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To find the values of the variables that satisfy all equations in the system 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 other.

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What is a linear equation?

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A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b.

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What does it mean for two equations to be equivalent?

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Two equations are equivalent if they have the same solution set, meaning they intersect at the same point(s) on a graph.

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How can you check the solution of a system of equations?

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Substitute the solution back into the original equations to verify that both equations are satisfied.

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What is a word problem?

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

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What is the importance of defining variables in word problems?

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Defining variables helps clarify what each symbol represents, making it easier to set up equations and solve the problem.