Solve Systems with Elimination Steps

Consider the system:

4x+3y=-1

5x+4y=1

Which we converted to:

16 x +​ 12y=​-4

-15x -​ 12y= -3

Combining the equations straight down gives us:

​ (a)   x+​ (b)   y=​ (c)  

Solving for x, we get x=​ (d)  

• 1

• 0

• -7

• 3

• 5

• -1

• -12

• -3

Consider the system:

4x+3y=-1

5x+4y=1

Since we now know that x=-7, solve for y:

4(​ (a)   )+3y=-1

​ (b)   +3y=-1

​ (c)   =​ (d)  

y=​ (e)  

• -7

• -28

• 3y

• 27

• 9

• 5

• 7

• -12

• 3

• y

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

• The  x

• The  y

• The  z

• The unknown

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

-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

Elimination, Part 1: How can you tell when you have infinite solutions when using elimination? (Pick two)

• All variables and constants will cancel out

• All variables will cancel out, but not the constants

• You will have a true statement like 0=0

• One variable and the constant will cancel out (x=0)

• You will have a false statement like 0=12

Elimination, Part 2: #1 (What is the best first step)

• Multiply the bottom equation by 3

• Multiply the bottom equation by -3

• Multiply the top equation by 3

• Multiply the top equation by -3