Solution - Linear equations with three unknowns

System of Linear Equations entered :

   [1]    3x + y = 8
   [2]    3y - z = 6
   [3]    x + z = 10

Solve by Substitution :

// Solve equation [3] for the variable  z 
 

  [3]    z = -x + 10

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

   [2]    3y - (-? +10) = 6
   [2]    3y = 16

// Solve equation [2] for the variable  ? 
 

  [2]    ? = -3y + 16

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

   [1]    3•(-3y+16) + y = 8
   [1]     - 8y = -40

// Solve equation [1] for the variable  y 

   [1]    8y = 40 

   [1]    y = 5 

// By now we know this much :

    ? = -3y+16
    y = 5
    z = -?+10

// Use the  y  value to solve for  ? 

    ? = -3(5)+16 = 1 

// Use the  ?  value to solve for  z 

    z = -(1)+10 = 9 

Solution :

 {?,y,z} = {1,5,9}