Solution - Linear equations with two unknowns

System of Linear Equations entered :

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

Graphic Representation of the Equations :

    y + 4x = -1        y + x = 2  

  
 

Solve by Substitution :

// Solve equation [2] for the variable  y 
 

  [2]    y = -x + 2

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

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

// Solve equation [1] for the variable  x 

   [1]    3x = - 3 

   [1]    x = - 1 

// By now we know this much :

    x = -1
    y = -x+2

// Use the  x  value to solve for  y 

    y = -(-1)+2 = 3 

Solution :

 {x,y} = {-1,3}