Elimination Method No Common Coefficients

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What is the Elimination Method in solving systems of equations?

Back

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you eliminate a variable using 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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved simultaneously.

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 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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CCSS.8.EE.C.8A

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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.

Tags

CCSS.8.EE.C.8A

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What is a common coefficient in the context of the Elimination Method?

Back

A common coefficient is a number that is the same in front of a variable in two different equations, which can be used to eliminate that variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

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

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Multiply the second equation by 2 to align the coefficients of x: 8x - 12y = 20. Then subtract the first equation from this new equation to eliminate x.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the first step in using the Elimination Method?

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The first step is to arrange the equations in standard form (Ax + By = C) and identify which variable to eliminate.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the significance of the solution to a system of equations?

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The solution to a system of equations represents the point(s) where the graphs of the equations intersect, indicating the values of the variables that satisfy all equations.

Tags

CCSS.8.EE.C.8B

Front

How do you check the solution of a system of equations?

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To check the solution, substitute the values of the variables back into the original equations to see if they hold true.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6