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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 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?

Back

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 the first step in using the Elimination Method?

Back

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

What do you do after eliminating one variable in a system of equations?

Back

After eliminating one variable, solve for the remaining variable, then substitute back to find the value of the eliminated variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a consistent system of equations?

Back

A consistent system of equations has at least one solution.

Tags

CCSS.8.EE.C.8B

Front

What is an inconsistent system of equations?

Back

An inconsistent system of equations has no solutions.

Tags

CCSS.8.EE.C.8B

Front

What is a dependent system of equations?

Back

A dependent system of equations has infinitely many solutions, as the equations represent the same line.

Tags

CCSS.8.EE.C.8B

Front

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

Back

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 significance of the coefficients in the Elimination Method?

Back

The coefficients determine how you can manipulate the equations to eliminate variables effectively.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What happens if the coefficients of the variable you want to eliminate are already opposites?

Back

If the coefficients are already opposites, you can directly add the equations to eliminate that variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6