Solution - Linear equations with three unknowns

System of Linear Equations entered :

   [1]    x + y + z = 8
   [2]    x - y + z = 2
   [3]    x - y - z = -4

Solve by Substitution :

// Solve equation [3] for the variable  x 
 

  [3]    x = y + z - 4

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

   [1]    (y +z -4) + y + z = 8
   [1]    2y + 2z = 12

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

   [2]    (y +z -4) - y + z = 2
   [2]    2z = 6

// Solve equation [2] for the variable  z 

   [2]    2z = 6 

   [2]    z = 3 

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

   [1]    2y + 2•(3) = 12
   [1]    2y = 6

// Solve equation [1] for the variable  y 

   [1]    2y = 6 

   [1]    y = 3 

// By now we know this much :

    x = y+z-4
    y = 3
    z = 3

// Use the  y  and  z  values to solve for  x 
  x = (3)+(3)-4 = 2 

Solution :

 {x,y,z} = {2,3,3}