Don't Hide From Linear Combinations...

Buzz Lightyear Will Save The Day!



 
 
 
 
 
Linear Combinations: 
If all variables have coefficients other than 1, we can use the multiplication and addition properties to find a combination of the linear equations that will eliminate a variable and this method is known as linear combination. 

Equations:
3x + 3y = 15
2x + 6y = 22
Work:
We can eliminate the y-variable if the 3y in the first equation were -6y. Therefore, we multiply both sides of the first 
equation by -2.
3x + 3y = 15 
-2(3x + 3y) = -2(15) 
-6x - 6y = -30 
-6x - 6y = -30 
2x + 6y = -22 

The two y's die and your left with:
-4x  = -8 
x = 2 

Substitute 2 for x in either of the original equations
and solve for y.
2x + 6y = 22 
2(2) + 6y = 22 
4 + 6y = 22 
6y = 18 
y = 3 

Solution of this system:
(2 , 3) 

Now you can plug in the x and the y in either of the original equations and check your answer!
3x + 3y = 15 
3(2) + 3(3) = 15 
6 + 9 = 15 
15 = 15 
Correct! 

 

 Here Are Five Practice Problems:

Quote From Rex & Buzz Lightyear:
"Wow! I didn't know this could be so easy!"

Equations: 
Answer:
1. 3x - 5y = 13
      x - 2y = 5
( 1 , -2 )
2. 7x + 2y = -1
    3x - 4y = 19
( 1 , -4 )
3. x + 2y = 6
   5x + 3y = 2
( -2 , 4 ) 
4. 2x + 3y = 7 
    3x + 4y = 10 
( 2 , 1 )
5. 5x - 3y = 16
    4x + 5y = -2
( 2 , -2 ) 

Are you still having trouble?
Mr. Ham has some steps that might help!

Steps For Using Linear Combination:

1. Write both equations in the form Ax + By = C
2. Clear any decimals or fractions.
3. Choose a variable to eliminate.
4. Make the chosen variable's terms additive inverse by multiplying one or both equations by a number.
5. Eliminate the variable by adding the equations.
6. Substitute to solve for the remaining variable.



 

Back To Home Page