Solving Systems of Equations with Elimination

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

What would be the first step in finding the solution using elimination?

• you cannot solve this using eliminiation

• cross out the 2x and 3x, because when you add them, they equal 0

• cross out the 2y and -2y because when you add them, they equal 0

• change to slope intercept form and graph

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.

Solve the system using elimination.

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.

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