Solving System of Equations Using Elimination

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

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

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

$$2x+3y=6$$  
$$-2x+8y=16$$  

• $$Addition$$  

• 
  $$Subtraction$$

• $$Multiplication\$$  

• $$Division$$  

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" 

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\$$  
  

Multiple Choice

Solve this system using elimination
4x+ 9y = 28
-4x -y = -28

• (-7,0)
• (6,0)
• (-6,0)
• (7,0)

Multiple Choice

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

• (-7,0)
• (6,0)
• (-6,0)
• (7,0)

Multiple Choice

What type of elimination could you use for this system of equations?

𝑥 − 6𝑦 = −18

−𝑥 + 10𝑦 = 30

• Addition

• Subtraction

• Simple Multiplication

• Complex Multiplication

Multiple Choice

What type of elimination would fit best for this system of equations?

6x + 5y = 4

6x – 7y = –20

• Simple Multiplication

• Subtraction

• Addition

• Complex Multiplication

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.