Systems of Equations Using Elimination

Solving Systems of Equations Using Elimination

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Multiple Select

What are the two methods to solve a system of equations we learned before break ?

• Substitution and Guess and Check

• Substitution and Elimination

• Substitution and Graphing

The Elimination Method

• Best when equations are "stacked" in standard form (Ax+By=C)

• Add or Subtract the equations to eliminate the variables (sometimes a littl magic multipliction is used too)

Multiple Choice

Which system of equations do you think is "stacked" ?

• 
  

   $2x+3y=6$  
  

  
   $-2x+4y=20$  
  

•  $5x+2=6y$  
   $y-1\ =4x$  
  

Multiple Choice

What operation do you think would eliminate the "x" variables in the system: 

 $2x+3y=6$  
 $-2x+8y=16$  

•  $Addition$  

• 
   $Subtraction$ 

•  $Multiplication\$  

•  $Division$  

• Add the equations

• The chosen variable will eliminate (disappear, cancel)

• Solve the new equation for the opposite variable

Multiple Choice

When we add the two equations, what is the new equation we've created ? 

 $3x+2y=7$  

 $-3x+4y=5$  

•  $6x+6y=12$  

•  $6y=75$  

•  $6y=12$  

Multiple Choice

Now that we have 6y=12, what do you think we do ? 

 $3x+2y=7$  

 $-3x+4y=5$  

• That's it  - that's the answer - piece of cake!

• Solve the equation  $6y=12$  and get y = 2, then substitute back into either equation to find "x" 

Open Ended

 $3x+2y=7$  

 $-3x+4y=5$  



Go ahead and find x. Type your answer here as an ordered pair!

Open Ended

Solve the system of equations by adding them together to eliminate a variable.  Be sure to write this in your notes. Input your answer as an ordered pair.  

 $3x-y\ =\ 12\$  

 $2x+y\ =\ 13$  

Poll

Look at the system of equations. How do you think you could start solving it. 

 $5x-3y\ =\ 16$  
 $x-3y=8$  

• Add em up!

• Subtract them!

• Multiply the bottom by -1 and then add em up!

Multiple Choice

If we multiply the bottom equation by negative one, what would that new equivalent equation be ? 

 $5x-3y\ =\ 16$  
 $x-3y=8$  

•  $-x\ -\ 3y\ =\ 8$  
  

•  $-x+3y\ =\ -8\$  

•  $-x\ +3y\ =\ 8\$  
  

Open Ended

What are two things you learned today? What questions do you still have??

Multiple Choice

What is the x-value for the solution to the following system of equations?

 $x+2y=13$  

 $-x+y=5$  

• -1

• 6

• 1

• -6

Multiple Choice

Which of the following is the correct solution to the system of linear equations?

 $5x+6y=50$  
 $x-6y=-26$  

• (6, 10/3)

• (6,5)

• (4,5)

• (4,-5)

Multiple Choice

What is the first step in solving the following system of linear equations using the elimination method?

 $x+y=2$  
 $2x+7y=9$  

• Add the x terms in the two equations and the y terms in the two equations so you get 3x + 8y = 11

• Multiply all terms in the top equation by 2 so that you  can eliminate the x terms

• Multiply the x in the first equation by -2 so you get -2x + y = 2

• Multiply all terms in the top equation by -2 so that you can eliminate the x terms. 

Multiple Choice

Describe the error in solving the system of equations using elimination:

• They eliminated the x terms when they should have eliminated the y terms.

• The subtracted 5x and x to get 4x, but they should have added the x terms to get 6x = 24.

• They added 16 and 8 to get 24, but they should have subtracted them to get 8 on the right side of the equation.

• They eliminated the y terms, but they couldn't because one is a negative and one is a positive.

Multiple Choice

Solve the system of linear equations using the elimination method.

 $-x+y=4$  

 $x+3y=4$  

• (-2,2)

• (2,-2)

• (-2,-2)

• (-2, 1/2)

Multiple Choice

In order to solve the following system of linear equations, which of the following is the correct first step to perform?
 $x+y=2$ 
 $2x+7y=9$  

• Multiply the entire first equation by 2

• Multiply the entire first equation by -2

• Multiply the entire second equation by -1

• Multiple the entire first equation by 7

Multiple Choice

Which of the following is the correct solution to the system of linear equations? Use the elimination method to solve.
 $10x-9y=46$  
 $-2x+3y=10$  

• (16,19)

• (19,-16)

• (-19,-16)

• (19,16)

Multiple Choice

What is the correct y-value for the solution to the following system of linear equations?
 $-3x-5y=-7$  
 $-4x+5y=14$  

• (1,2)

• (-1,2)

• (1,-2)

• (-1,-2)

Multiple Choice

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

• (-7,0)
• (6,0)
• (-6,0)
• (7,0)

Multiple Choice

Solve by elimination:
3x+7y=23

-3x-7y=-17

• No solution
• ARN
• (-3,3)
• (3,3)

Multiple Choice

Solve by elimination:
7x+y=-9

-3x-y=5

• No solution
• (1,8)
• (-2,-3)
• (-1,-2)

Multiple Choice

Solve using elimination. 
 4x + 8y = 20
-4x + 2y = -30

• (-7,1)
• (2,-5)
• (-2,5)
• (7,-1)

Multiple Choice

What Are These Called?

• Penguins
• Minions
• Gru
• Animated Children

Multiple Choice

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

• (-7,0)
• (6,0)
• (-6,0)
• (7,0)