Solution - Linear equations with three unknowns

System of Linear Equations entered :

   [1]    6r - 5s - 2t = -11
   [2]    2r - s - 4t = -9
   [3]    4r - 5s + 5t = -4

Solve by Substitution :

// Solve equation [2] for the variable  s 
 

  [2]    s = 2r - 4t + 9

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

   [1]    6r - 5•(2r-4t+9) - 2t = -11
   [1]    -4r + 18t = 34

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

   [3]    4r - 5•(2r-4t+9) + 5t = -4
   [3]    -6r + 25t = 41

// Solve equation [3] for the variable  t 
 

  [3]    25t = 6r + 41

  [3]    t = 6r/25 + 41/25

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

   [1]    -4r + 18•(6r/25+41/25) = 34
   [1]    8r/25 = 112/25
   [1]    8r = 112

// Solve equation [1] for the variable  r 

   [1]    8r = 112 

   [1]    r = 14 

// By now we know this much :

    r = 14
    s = 2r-4t+9
    t = 6r/25+41/25

// Use the  r  value to solve for  t 

    t = (6/25)(14)+41/25 = 5 

// Use the  r  and  t  values to solve for  s 
  s = 2(14)-4(5)+9 = 17 

Solution :

 {r,s,t} = {14,17,5}