Solving Systems of Equations Using Elimination

4x +  8y = 20

-4x + 2y = -30

When you solve these equations using the elimination method, which variable will be eliminated?

• The  x

• The  y

• The  z

• The unknown

-4x - 6y = -24

4x - 7y = - 54

Let's combine (add) these 2 equations to ELIMINATE the x variable. What would our combined equations be?

• -1y = 30

• 13y = -30

• -1y = -78

• -13y = -78

The coefficients of the eliminated variable must be _____.

• opposites

• the same

• distinct

• does not matter

Say you wanted to eliminate x from the system shown. How would you do it?

• Add the equations without doing any multiplication.

• Multiply the first equation by 2 and the second equation by 3, then add the equations.

• Multiply the first equation by negative 2 and the second equation by 3, then add the equations.

• Multiply the first equation by 3 and the second equation by negative 2, then add the equations.

Solve the system using elimination.

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Which of the following could be a correct first step in solving the system shown? Select all that apply.

• Multiply the first equation by 2, then add the result to the third equation.

• Multiply the second equation by 2, then add the result to the third equation.

• Add the first and second equation.

• Add the first and third equation.

• Add the second and third equation.

Solve the system using elimination.

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Look for ____ when determining which variable to eliminate. Select all that apply

• same coefficeints with opposite signs

• easy numbers to multiply to (common factors)

• different coefficients

• vertical alignment of like terms

To find the second variable, substitute the x or y you solved for into one of the ____.

• original equations

• one of the manipulated equations

• the top equation, always

• the bottom equation, always

Order the algorithm (steps) to elimination

• Align like terms vertically

• Determine the variable to eliminate

• multiply equation(s) to have opposite coefficients, if necessary

• add vertically

• Solve for variable