Stephane is in a freestyle aerial skiing competition. The equation h = -16t^2 + 30t + 10 models Stephane’s height, h, in feet, t seconds after leaving the ramp. How long is Stephane in the air? When will she reach a height of 15 feet? To earn bonus points in the competition you must reach a minimum height of 20 feet. Will Stephane earn bonus points?

1 )
1st and 2nd equation (multiply 1st by -2 ):
-2x - 10 y + 8 z = 20
2 x -  y    + 5 z = -9

       - 11 y + 13 z = 11  /  * ( -20 )
1st and 3rd:
- 2 x - 10 y + 8 z = 20
   2 x - 10 y - 5 z = 0

         - 20 x + 3 z = 20  /  * 11
       
         220 y - 260 z = -220
        - 220 y + 33 z = 220
       
                       z = 0,      y = -1,        x = - 5
2 )  
       2 x - y + 5 = -4
       - 2 x + 3 y - 5 = - 10
       Substitution: y = 2 x + 9
       - 2 x + 3(2 x + 9 ) = -5
        4 x = - 32,          x = -8,    y = -7,   z = 5
3 )
      x + y + z = 11
   1.5 x+3 y +1.5 z = 21
      x = 2 y
   
      3 y + z = 11  / * (-2)
      6 y + 1.5 z = 21
   
     - 6 y - 2 z = -22
       6 y + 1.5 z = 21
     
                 -0.5 z = -1,           z = 2,   y = 3,   z = 6
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