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 solve a system of equations using substitution?

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1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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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 variable.

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

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A system has no solution if the equations represent parallel lines that never intersect.

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

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A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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How can 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 set them equal to each other.

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

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Identify the unknowns and define them as variables.

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In the problem 'The difference of a and b is 3', how can this be expressed as an equation?

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a - b = 3.

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In the problem 'The sum of a and b is 13', how can this be expressed as an equation?

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a + b = 13.

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How do you check your solution after solving a system of equations?

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