Solving Systems by Elimination

Solving Systems by Elimination

Objective: Solve a system of equations by elimination

​System of Equations: a collection of two or more equations with the same set of unknowns (variables).

​Example:

​4x - y = -6

​5x + y = -21

Multiple Choice

At what point do these two lines cross?

• (3,4)

• (4,3)

• (-3,4)

• (-4,3)

• (3,-4)

2x - y = 2

x + y = 7​

EXAMPLE

​What if we don't have a graph.

1. Line up the x, the y, and the equal sign.

2. Look to see if the variables are the same/opposite.

   1. If YES - Move to Step 3

   2. If NO. - Multiply one or both equation by a constant (LCM) to make the coefficients the same or opposite.

3. Add or Subtract the TWO equations to eliminate one of the variables.

4. Solve for the remaining variable

5. Substitute your answer in one of the original equations

6. Check your answer.

7. Write final answer as an ordered pair.

STEPS TO SOLVE

Let's Explore Each Step

line up the x & y & the equal sign.​

Multiple Choice

Look at the system below. Is the x & y lined up?

$$3x=4y-7\$$  

$$3x+7y=11$$  

• YES

• NO

Multiple Choice

Is the System Lined up?

$$4y\ -\ 3x=12$$  

$$y+3x=0$$  

• No

• YES

Let's Explore Each Step

​

ONE VARIABLE MUST BE ELIMINATED!!!!!!!!!

​

Multiple Choice

4x +  8y = 20
-4x + 2y = -30
Which variable will be eliminated?

• The  x
• The  y
• The  z
• The unknown

Let's Explore Each Step

look to see if any of the coefficients are the same/opposite.

Multiple Choice

Are any of the coefficients same or opposite?

2x - 6y = 20

2x + 5y = -11

• Same

• Opposite

• Neither

Multiple Choice

Are any of the coefficients same or opposite?

x - y = 11

2x + y = 19

• Same

• Opposite

• Neither

Multiple Choice

Are any of the coefficients same or opposite?

4x+ 9y = 28

-4x -y = -28

• Same

• Opposite

• Neither

Let's Explore Each Step

Add or Subtract the TWO equations to eliminate one of the variables.

Multiple Choice

9x-3y=-3

-5x+3y=-1

Would you add or subtract to eliminate the variable (Get ZERO)

• ADD

• SUBTRACT

Multiple Choice

10x-8y=-30

-10x+9y=25

Would you add or subtract to eliminate the variable (Get ZERO)

• ADD

• SUBTRACT

Let's Explore Each Step

If NO. - multiply one or both equation by a constant (LCM) to make the coefficients the same or opposite.

Multiple Choice

Solve by elimination
4x-6y= -6
-2x-12y= -12

• (0,1) 
• (1,0)
• (1,1)
• (2,1)

Multiple Choice

Solve by elimination 
2x+9y= -7 
6x-3y= 9 

• (-1, -1) 
• (2,-1)
• (1,1)
• (1,-1)

Multiple Choice

Macy starts with $20 in her bank account and she saves $5 each week. Robby has $100 in his bank account, and he saves $2.50 each week. After how many weeks will Macy and Robby have the same amount in their accounts and how much money will that be? Write a system of equations to solve.

• 25 weeks; $160

• 32 weeks; $180

• 20 weeks; $120

• 22 weeks; $135

Multiple Choice

Ride and Transport are two new ride sharing companies in Colorado. Ride is charging $2 for pick up fees and then $2.50 per mile. Transport is charging only $2.70 per mile. How many miles will it take for both companies to charge the same amount? Write a system of equations to solve.

• 27 miles

• 10 miles

• 270 miles

• 100 miles

Poll

How are you feeling about this topic (elimination) so far?

• I understand!

• I need more practice, but I'm getting it

• I do not know where to begin