Math Made Easy
+ the help - the nonsense
by: Cutie Cat

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

3x - 2 ( 5 - 4x) = 12
   3x - 10 + 8x = 12
         11x - 10 = 12
             + 10 = + 10
               11x = 22
        (11x / 11) = (22 / 11)
                    x = 2

y = 5 - 4 (2)
y = 5 - 8
y = -3

(2,-3)

The given equation can easily be solved through substitution.  To begin write the equation... but instead of writing the variable "y", substitute it with the y equals formula.  Then multiply the parenthetical formula by the outside number, add all like terms.  When a number as well as the variable remains, "kill" the extra number.  Whatever you do to rid the number on one side, do the exact same thing to the other.  Then to find the variable's value divide on each side until you are left with the x.

 
 
EXAMPLE
EXPLANATION
3x - 5y = 13
x - 2y = 5

 3x - 5y = 13
-3[x - 2y = 5]

  3x - 5y = 13
-3x + 6y = -15
          y = -2

x - 2 (-2) = 5
    x + 4 = 5
       - 4    - 4>
          x = 1

( 1, -2)
 In this particular type problem it is necessary to find a number that is able to cancel out one of the variables.  So in order to to get rid of the x the bottom problem must be multiplied by -3.  With the xs gone the y should now be solved for. Once y is solved for the number of the y (-2) should be be placed into one of the original equations . . . (x - 2y = -5) so then the problem appears to look as such :  (x - 2 [-2] = 5).  Then it becomes simple to solve for x. 
 
EXAMPLE
EXPLANATION
The measure of one of two supplementary angles is 8 degrees greater than three times the other.  Find the measure of the larger of the two angles. 

                  x = larger    y = smaller
x + y = 180 . . . x = 180 - y
x = 3y + 8

180 - y = 3y + 8
  -8              - 8
172 - y  = 3y
     + y    +y
      172 = 4y
(172 / 4) = (4y / 4)
       43 = y

x = 180 - y
x = 180 - 43
x = 137

(137, 43)
 The thing of main importance when working a word problem is to not let it be intimidating. Now, you need to set up the problem, know that supplementary angles are 180 degrees. . . ( x + y = 180), you have then discovered the "hidden" number needed to work the problem. The x is 8 degrees greater than three times the y . . . (x = 3y + 8).  Now, substitute the x with its y equvilant . . . (180 - y = 3y + 8 ).  Then get all the ys on one side and all the unvaried numbers on the other.  Remeber that  whatever is done to one side must be done to the other.  Once the equation is balanced (172 = 4y) divide varied number on each side, then the y is found.  In order to find the x plug the y into an original equation, then solve.  Its as easy as that. 

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