Elimination Method No Common Coefficients

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What is the Elimination Method in solving systems of equations?

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The Elimination Method is a technique used to solve systems of linear equations by eliminating one variable, allowing for the solution of the other variable.

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How do you eliminate a variable in the Elimination Method?

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To eliminate a variable, you can multiply one or both equations by a number so that the coefficients of one variable are opposites, allowing you to add or subtract the equations.

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What is a system of linear equations?

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A system of linear equations is a set of two or more linear equations with the same variables.

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

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A system of equations has no solution if 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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A system of equations has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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What is a common coefficient in a system of equations?

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A common coefficient is a number that is the same for a variable in both equations of a system, which can simplify the elimination process.

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How can you solve the system: 8x - 7y = -5 and 4x - 6y = 10 using the Elimination Method?

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Multiply the second equation by 2 to get 8x - 12y = 20. Then subtract the first equation from this to eliminate x, leading to -5y = 25, so y = -5. Substitute y back to find x.

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What is the first step in using the Elimination Method?

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The first step is to align the equations and decide which variable to eliminate.

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How do you check your solution after using the Elimination Method?

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To check your solution, substitute the values of the variables back into the original equations to see if both equations are satisfied.

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What is the solution to the system: x - y = 11 and 2x + y = 19?

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The solution is (10, -1).