Solution - Linear equations with three unknowns

System of Linear Equations entered :

   [1]    -4x + 3y + 2z = -12
   [2]    -8x - 3y - 3z = -24
   [3]    16x - 3y - 6z = 48

Solve by Substitution :

// Solve equation [3] for the variable  x 
 

  [3]    16x = 3y + 6z + 48

  [3]    x = 3y/16 + 3z/8 + 3

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

   [1]    -4•(3y/16+3z/8+3) + 3y + 2z = -12
   [1]    9y/4 + z/2 = 0
   [1]    9y + 2z = 0

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

   [2]    -8•(3y/16+3z/8+3) - 3y - 3z = -24
   [2]     - 9y/2 - 6z = 0
   [2]     - 9y - 12z = 0

// Solve equation [1] for the variable  z 
 

  [1]    2z = -9y 

  [1]    z = -9y/2 

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

   [2]     - 9y - 12•(-9y/2) = 0
   [2]    45y = 0

// Solve equation [2] for the variable  y 

   [2]    45y = 0 

   [2]    y = 0 

// By now we know this much :

    x = 3y/16+3z/8+3
    y = 0
    z = -9y/2

// Use the  y  value to solve for  z 

    z = -(9/2)(-0/32766) = 0 

// Use the  y  and  z  values to solve for  x 
  x = (3/16)(-0/32766)+(3/8)(0)+3 = 3 

Solution :

 {x,y,z} = {3,0/32766,0}