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

Front

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

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To eliminate a variable, you can add or subtract the equations in such a way that one of the variables cancels out.

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 an infinite number of solutions?

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An infinite number of solutions means that the equations represent the same line, and thus every point on that line is a solution.

Tags

CCSS.8.EE.C.8A

Front

What is the graphical interpretation of the solution to a system of equations?

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The solution to a system of equations is the point where the graphs of the equations intersect.

Tags

CCSS.8.EE.C.8B

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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 manipulate them to make the coefficients of one variable the same.

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What should you do if the coefficients of the variable you want to eliminate are not the same?

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You can multiply one or both equations by a suitable number to make the coefficients equal.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it indicate if two lines are parallel when solving a system of equations?

Back

If two lines are parallel, it indicates that there is no solution to the system of equations, as they do not intersect.

Tags

CCSS.8.EE.C.8A

Front

How can you check your solution after using the elimination method?

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You can check your 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 result of the elimination method if the two equations are identical?

Back

If the two equations are identical, it indicates that there are infinitely many solutions.

Tags

CCSS.8.EE.C.8B