Solution - Linear equations with three unknowns

System of Linear Equations entered :

   [1]    4a + 4b - c = 2
   [2]    3a + 2b + c = -3
   [3]    6a - 4b - 3c = 6

Solve by Substitution :

// Solve equation [2] for the variable  c 
 

  [2]    c = -3a - 2b - 3

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

   [1]    4a + 4b - (-3a-2b-3) = 2
   [1]    7a + 6b = -1

// Plug this in for variable  c  in equation [3]

   [3]    6a - 4b - 3•(-3a-2b-3) = 6
   [3]    15a + 2b = -3

// Solve equation [3] for the variable  b 
 

  [3]    2b = -15a - 3

  [3]    b = -15a/2 - 3/2

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

   [1]    7a + 6•(-15a/2-3/2) = -1
   [1]    -38a = 8

// Solve equation [1] for the variable  a 

   [1]    38a = - 8 

   [1]    a = - 4/19 

// By now we know this much :

    a = -4/19
    b = -15a/2-3/2
    c = -3a-2b-3

// Use the  a  value to solve for  b 

    b = -(15/2)(-4/19)-3/2 = 3/38 

// Use the  a  and  b  values to solve for  c 
  c = -3(-4/19)-2(3/38)-3 = -48/19 

Solution :

 {a,b,c} = {-4/19,3/38,-48/19}