Solution - Linear equations with three unknowns

System of Linear Equations entered :

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

Solve by Substitution :

// Solve equation [3] for the variable  z 

   [3]    z = 3 

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

   [1]    x - y + 2•(3) = 4
   [1]    x - y = -2

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

   [2]    y + 2•(3) = -2
   [2]    y = -8

// Solve equation [2] for the variable  y 

   [2]    y = - 8 

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

   [1]    x - (-8) = -2
   [1]    x = -10

// Solve equation [1] for the variable  x 

   [1]    x = - 10 

// By now we know this much :

    x = -10
    y = -8
    z = 3

We are done

Solution :

 {x,y,z} = {-10,-8,3}