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 they reflect the problem's context.

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What does it mean when two variables are dependent in a system of equations?

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It means that the value of one variable can be expressed in terms of the other, indicating a relationship between them.

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

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It means that the lines represented by the equations are parallel and never intersect.

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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 every point on that line is a solution.

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

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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 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 do you identify variables in a word problem?

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Look for quantities that change or are unknown, and assign a variable to each of these quantities.