Solving Systems of Linear Equations WORD PROBLEMS

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What is a system of linear equations?

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A set of two or more linear 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 to solve a system of linear 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 the substitution method in solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted 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 equations are added or subtracted 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.

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

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The equations represent the same line, meaning every point on the line is a solution.

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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 a word problem involving a system of equations?

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A real-life scenario that can be modeled with two or more equations to find unknown values.

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Example of a system of equations from a word problem: 'The cost of 5 apples and 2 bananas is $1.50. The cost of 3 apples and 1 banana is $0.90.'

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5a + 2b = 1.50, 3a + 1b = 0.90