There is HO HO HO...PE in  learning       Equations...
 
 
 
WHAT IS THE PURPOSE OF THIS?  

   Having problems in algebra? having  
problems understanding or learning how to  
substitute or with linear combination. Hi my  
name is Jessica and I am making this website  
to help you learn how to do these equations  
with ease.  And also to help you gain  
knowledge of Algebra and how it works. 
 

 
  Substitution: "PLUG IT IN" 
      * indicates the answer: 

               y = 3x  
               x + y = 8  
               x + 3x = 8  
               4x = 8 
4x = 8 
                4    4 
               *x = 2  

               y = 3(2)  
               *y = 6  

HERE'S ANOTHER EXAMPLE: DO IT YOURSELF:  

               y = 5 - 4x 
               3x - 2y = 12 

* remember you know what y equals so plug y into the under equation to find x. Then work from there. 
 

     click here to visit my classmates pages 

 

 

  How to substitute: Substituting is the same thing as plugging in a nHow to substitute: Substituting is the same thing as plugging in a number into an equation to find an x and a y. i am going to take you step by step using the example on the left.  

1) the equation is: y = 3x 
                           x + y = 8 
2) You know that y = 3x so you can plug in 3x into the equation under the y = 3x  where the y is. like this:  
x + (3x) = 8 the 3x is now where the y used to be. 

3) now solve, add like terms. 

4) 4x = 8 

5) now divide to get x alone 

6) 4x = 8 
    4    4 

7) x = 2 now you have your answer for x!! 

8) now you have to find a y as well...  

9) you now know that x = 2  

10) so now you have to plug in x into the other equation to now find y 

11) y = 3(2) 

12) y = 6  NOW YOUR DONE!!  

 
             LINEAR COMBINATION!!
                        and... Word problems.
 
 
Linear combination is very similar to substitution but also very different at the same time. Instead of finding a number that goes into one equation or a number that  just goes into the  x or y equation  you have got to find a number that goes into both equations.  ANSWER TO " TRY IT YOURSELF" SUBSTITUTION QUESTION :  (2, -3)

 

EXAMPLE OF LINEAR COMBINATION:  

    2x + 3y = 7 
    3x + 4y =10  

    3 ( 2x + 3y = 7) 
   -2 ( 3x + 4y = 10) 

    6x + 9y = 21 
   -6x - 8y = -20 

     y = 1 

     2x  = 4 
      2      2 

     x = 2 

 
 

 

1) 2x + 3y = 7  
     3x + 4y = 10 
 this is the equation you need to find a number that is mulitplyed by both equations will cancel each other out 

 2) 3(2x + 3y = 7) 
     -2( 3x + 4y = 10) 
 3 times 2 = 6 and -2 times 3x = -6 6 and -6 cancel eachother out to maake this equation possible to solve. 

 3) 6x + 9y = 21 
    -6x - 8y = -20 
 now you can cancel out the x's and you are left with: 

4) 9y = 21 
   -8y = -20 

5) 1y = 1 

6) 1y = 1 
     1     1 
 now divide y by 1 to get y by it'self  

7) y = 1 

8) 2x + 3(1) = 7 
 plug 1 into one of the equations 

9) 2x + 3 = 7 

10) 2x + 3 - 3 = 7- 3 
 subtract 3 from each side to get 2x by it'self 

11) 2x = 4 

12) 2x = 4 
       2     2 
 divide each side by 2 to get x by it'self 

13) x = 2 

14) your answer is: ( 2, 1) 

 
 Word Problems: 

One day a the elves in santa's workshop made 45 presents, one kind sold for $8.50 and another kinda sold for $ 9.75. In all, $398.75 was taken in. How many of each kind were sold? 

  

8.50x + 9.75y = 398.75
 x + y = 45 
 x = -y + 45 plug x in to the original equation 
 8.50 ( -y + 45) + 9.75 y = 398.75
 -8.50y + 382.50 + 9.75y = 398.75
 1.25y + 382.50 = 398.75
 -382.50                 - 382.50
1.25y  =  16.25
1.25          1.25
y= 13 plug y into the original equation
x+ 13 = 45 
-13        -13
x= 32