Solving Systems of Equations Using Elimination

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??