Writing Systems of Equations (Word Problems) HW

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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

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What does it mean to solve a system of equations?

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Finding the values of the variables that satisfy all equations in the system simultaneously.

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What is a word problem in mathematics?

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A problem that presents a mathematical situation in the form of a narrative or real-life scenario.

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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, often represented by letters like x and y.

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What is the first step in solving a word problem involving a system of equations?

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Read the problem carefully and identify the variables and relationships.

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What does it mean to write an equation from a word problem?

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Translating the relationships and conditions described in the problem into a mathematical equation.

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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 back into the original equations to see if they hold true.

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What is the substitution method in solving systems of equations?

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A method where you solve one equation for one variable and substitute that expression into the other equation.

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What is the elimination method in solving systems of equations?

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A method where you add or subtract 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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The lines represented by the equations are parallel and never intersect.