Solution - Linear equations with three unknowns

System of Linear Equations entered :

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

Equations Simplified or Rearranged :

   [1]    3x - y = 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 [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]    3x - (-8) = 4
   [1]    3x = -4

// Solve equation [1] for the variable  x 

   [1]    3x = - 4 

   [1]    x = - 4/3 

// By now we know this much :

    x = -4/3
    y = -8
    z = 3

We are done

Solution :

 {x,y,z} = {-4/3,-8,3}