Solve the system of equations 5x+9y+9z=5 4x+9y+6z=10 2x+2y+5z=9

{x,y,z} = {-116,28,37}

Step-by-step explanation:

// Solve equation [3] for the variable  z  

 [3]    5z = -2x - 2y + 9

 [3]    z = -2x/5 - 2y/5 + 9/5

// Plug this in for variable  z  in equation [1]

  [1]    5x + 9y + 9•(-2x/5-2y/5+9/5) = 5

  [1]    7x/5 + 27y/5 = -56/5

  [1]    7x + 27y = -56

// Plug this in for variable  z  in equation [2]

  [2]    4x + 9y + 6•(-2x/5-2y/5+9/5) = 10

  [2]    8x/5 + 33y/5 = -4/5

  [2]    8x + 33y = -4

// Solve equation [2] for the variable  y  

 [2]    33y = -8x - 4

 [2]    y = -8x/33 - 4/33

// Plug this in for variable  y  in equation [1]

  [1]    7x + 27•(-8x/33-4/33) = -56

  [1]    5x/11 = -580/11

  [1]    5x = -580

// Solve equation [1] for the variable  x  

  [1]    5x = - 580  

  [1]    x = - 116

// By now we know this much :

   x = -116

   y = -8x/33-4/33

   z = -2x/5-2y/5+9/5

// Use the  x  value to solve for  y  

   y = -(8/33)(-116)-4/33 = 28

// Use the  x  and  y  values to solve for  z  

 z = -(2/5)(-116)-(2/5)(28)+9/5 = 37

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│Hope this helped  │    

│~Derelis │

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