Elimination Method

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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 remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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How do you eliminate a variable in a system of equations?

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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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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

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A system has infinite solutions when the equations represent the same line, meaning every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

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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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you check if your solution to a system of equations is correct?

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You can check the solution by substituting the values back into the original equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the significance of the coefficients in the Elimination Method?

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The coefficients determine how the equations can be manipulated to eliminate a variable; they must be adjusted to create opposites.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it indicate if two equations in a system are parallel?

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If two equations are parallel, it indicates that there is no solution, as the lines will never intersect.

Tags

CCSS.8.EE.C.8A

Front

What is the result of solving the system: 4x + 9y = 28 and -4x - y = -28?

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The result is (7, 0), which is the point of intersection of the two lines.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

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The solution is (10, -1), which satisfies both equations.

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CCSS.HSA.REI.C.9

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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 when the equations represent parallel lines that do not intersect.

Tags

CCSS.8.EE.C.8A