Solution - Linear equations with two unknowns

System of Linear Equations entered :

   [1]    x + 2y = 5
   [2]    x - 2y = 3

Graphic Representation of the Equations :

    2y + x = 5        -2y + x = 3  

  
 

Solve by Substitution :

// Solve equation [2] for the variable  x 
 

  [2]    x = 2y + 3

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

   [1]    (2y+3) + 2y = 5
   [1]    4y = 2

// Solve equation [1] for the variable  y 

   [1]    4y = 2 

   [1]    y = 1/2 

// By now we know this much :

    x = 2y+3
    y = 1/2

// Use the  y  value to solve for  x 

    x = 2(1/2)+3 = 4 

Solution :

 {x,y} = {4,1/2}