Linear Systems Elimination Method

Solving Systems of Equations Using Elimination

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\$$  

• $$Division$$  

 $3x+2y=7$  

 $-3x+4y=5$  

If a variable has opposite coefficients:

• 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??