Systems of Equations Elimination Steps

Solve the system to find y:

x + 6y = 17

-x + 3y = -8

• y = 2

• y = 1

• y = 11

• no solution

-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

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

The coefficients of the eliminated variable must be _____.

• opposites

• the same

• distinct

• does not matter

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

• Solve for variable

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

• Determine the variable to eliminate

• add vertically

• Align like terms vertically

Let's multiply the top equation by -2. What would be our new equation?

2x + 3y = 12

4x - 7y = - 54

• 4x - 6y = -24

• -4x - 6y = 12

• -4x - 6y = 24

• -4x - 6y = -24

Solve by elimination:
4x+9y=28
-4x-y=-28

• (-7,0)

• (6,0)

• (-6,0)

• (7,0)

What variable do you eliminate?

4x + 8y = 20

−4x + 2y = −30

• X because they have opposite signs

• Y because they have opposite signs