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9x + 5y - z = -11 6x + 4y + 2z = 2 2x – 2y + 4z = 4

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9x + 5y - z = -11 6x + 4y + 2z = 2 2x – 2y + 4z = 4 Powered By Docstoc
					        9x + 5y - z = -11
        6x + 4y + 2z = 2
        2x – 2y + 4z = 4

 Pick a variable to eliminate.

z would be a great choice

We’ll start with the first 2 equations.
            9x + 5y - z = -11
            6x + 4y + 2z = 2
            2x – 2y + 4z = 4

            9x + 5y - z = -11
            6x + 4y + 2z = 2

     Multiply the first equation by 2
           18x + 10y - 2z = -22
            6x + 4y + 2z = 2
Add them   24x + 14y      = -20
              Now we will set this
              one aside and go back
              to the original problem.
           9x + 5y - z = -11
           6x + 4y + 2z = 2       This time we will
           2x – 2y + 4z = 4       use the last two
                                  equations
           6x + 4y + 2z = 2
           2x – 2y + 4z = 4
    Multiply the first equation by -2
            -12x – 8y - 4z = -4
             2x – 2y + 4z = 4
Add them   -10x – 10y     = 0
      Now we will use this one and
      the one set aside.
   24x + 14y = -20
   -10x – 10y = 0
Multiply the first equation by 5
Multiply the second equation by 7.
        120x + 70y = -100
         -70x – 70y = 0
         50x            = -100
         50                50
               x = -2
       24x + 14y = -20
       -10x – 10y = 0 x = -2

      -10(-2) – 10y =         0
           20 – 10y = 0
          -20         -20
               -10y = -20
               -10    -10
                  y = 2
Now, take these values and plug them into one of
the original equations.
9x + 5y - z = -11
6x + 4y + 2z = 2
2x – 2y + 4z = 4

x = -2, y = 2
2x – 2y + 4z = 4
2(-2) – 2(2) + 4z = 4
   -4 – 4 + 4z = 4
                        (-2, 2, 3)
    -8 + 4z = 4
    +8       +8
         4z = 12
          z=3

				
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posted:3/26/2013
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