Elimination Method

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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

What is the first step in using the Elimination Method?

Back

The first step is to manipulate the equations to align coefficients of one variable so that they can be eliminated when the equations are added or subtracted.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you create a zero pair in the Elimination Method?

Back

To create a zero pair, you multiply one or both equations by a number so that the coefficients of one variable are opposites, allowing them to cancel each other out.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to 'cross out' a variable in the Elimination Method?

Back

'Crossing out' a variable means to eliminate it from the equations by adding or subtracting the equations, resulting in a single equation with one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

In the equation 4x + 3y = 1 and x - 3y = -11, which variable can be eliminated first?

Back

The variable 3y can be eliminated by aligning the coefficients of y in both equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system of equations x - y = 11 and 2x + y = 19 using the Elimination Method?

Back

The solution is (10, -1).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a 'zero pair' in the context of the Elimination Method?

Back

A zero pair occurs when two terms in an equation cancel each other out, resulting in a sum of zero.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How can you determine which variable to eliminate in a system of equations?

Back

You can determine which variable to eliminate by looking for the variable with coefficients that can easily be manipulated to create opposites.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the purpose of multiplying an equation in the Elimination Method?

Back

Multiplying an equation is done to adjust the coefficients of a variable so that they can be eliminated when the equations are combined.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the result of eliminating a variable in a system of equations?

Back

The result is a single equation with one variable, which can be solved to find the value of that variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6