Solution - Linear equations with four unknowns

System of Linear Equations entered :

   [1]    2x + 3y + 7z = 8
   [2]    x - y + 2z = 4
   [3]    -3x + 2y + z = 10
   [4]    x + 3y + 12z = 26

Solve by Substitution :

// Solve equation [4] for the variable  x 
 

  [4]    x = -3y - 12z + 26

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

   [1]    2•(-3y-12z+26) + 3y + 7z = 8
   [1]     - 3y - 17z = -44

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

   [2]    (-3y-12z+26) - y + 2z = 4
   [2]     - 4y - 10z = -22

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

   [3]    -3•(-3y-12z+26) + 2y + z = 10
   [3]    11y + 37z = 88

// Solve equation [3] for the variable  z 
 

  [3]    37z = -11y + 88

  [3]    z = -11y/37 + 88/37

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

   [1]     - 3y - 17•(-11y/37+88/37) = -44
   [1]    76y/37 = -132/37
   [1]    76y = -132

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

   [2]     - 4y - 10•(-11y/37+88/37) = -22
   [2]     - 38y/37 = 66/37
   [2]     - 38y = 66

// Solve equation [1] for the variable  y 

   [1]    76y = - 132 

   [1]    y = - 33/19 

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

   [2]     - 38•(-33/19) = 66
   [2]    0 = 0 =>  Infinitely many solutions 

Infinitely many solutions