What are the coordinates of three points that lie on both planes of 20x+15y+12z=60 and 10x+30y+12z=60

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tadriana1999 tadriana1999

04-03-2015
Mathematics

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What are the coordinates of three points that lie on both planes of 20x+15y+12z=60 and 10x+30y+12z=60

Sagot :

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Panoyin Panoyin · Answer 1 · 2015-03-04T20:56:16-05:00

20x + 15y + 12z = 60 ⇒ 20x + 15y + 12z = 60
10x + 30y + 12z = 60 ⇒ 20x + 60y + 24z = 120
      -45y - 12z = -60
-45y + 45y - 12z = -60 + 45y
   -12z = -60 + 45y
      -12    -12
      z = 5 - 45/12y
      20x + 15y + 12(5 - 45/12y) = 60
      20x + 15y + 12(5) - 12(45/12y) = 60
   20x + 15y + 60 - 45y = 60
   20x + 15y - 45y + 60 = 60
   20x - 30y + 60 = 60
   -60   -60
   20x - 30y = 0
      20x - 20x - 30y = 0 - 20x
       -30y = -20x
      -30 -30
      y = 2x/3
      20x + 15(2x/3) + 12(5 - 45/12y) = 60
      20x + 10x + 60 - 45y = 60
      30x - 45y + 60 = 60
      -60 -60
      30x - 45y = 0
      30x - 45y + 45y = 0 + 45y
   30x = 45y
      30 30
   x = 3/2y
      20(3/2y) + 15(2x/3) + 12(5 - 45/12y) = 60
   30y + 10x + 60 - 45y = 60
       10x + 30y - 45y + 60 = 60
   10x - 15y + 60 = 60
       -60 -60
   10x - 15y = 0
   10(3/2y) + 30(2x/3) + 12(5 - 45/12y) = 60
      15y + 20x + 60 - 45y = 60
      20x + 15y - 45y + 60 = 60
          20x - 30y + 60 = 60
      -60 -60
      20x - 30y = 0
   10x - 15y = 0 ⇒ 20x - 30y = 0
   20x - 30y = 0 ⇒ 20x - 30y = 0
      -60y = 0
   -60 -60
   y = 0
   10x - 15(0) = 0
   10x - 0 = 0
      +0 +0
      10x = 0
       10 10
      x = 0
      20x + 15y + 12z = 60
      20(0) + 15(0) + 12z = 60
      0 + 0 + 12z = 60
      0 + 12z = 60
      12z = 60
   12    12
      z = 5
       (x, y, z) = (0, 0, 5)

Sagot :

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