Solution - Linear equations with two unknowns

System of Linear Equations entered :

   [1]    2x + 3y = 6
   [2]    x - y = 1/2

// To remove fractions, multiply equations by their respective LCD

     Multiply equation [2] by 2


// Equations now take the shape:

   [1]    2x + 3y = 6
   [2]    2x - 2y = 1

Graphic Representation of the Equations :

    3y + 2x = 6        -2y + 2x = 1  

  
 

Solve by Substitution :

// Solve equation [2] for the variable  x 
 

  [2]    2x = 2y + 1

  [2]    x = y + 1/2

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

   [1]    2•(y +1/2) + 3y = 6
   [1]    5y = 5

// Solve equation [1] for the variable  y 

   [1]    5y = 5 

   [1]    y = 1 

// By now we know this much :

    x = y+1/2
    y = 1

// Use the  y  value to solve for  x 

    x = (1)+1/2 = 3/2 

Solution :

 {x,y} = {3/2,1}