Solution - Linear equations with two unknowns

System of Linear Equations entered :

   [1]    6x - 3y = 8
   [2]    4x + 7y = 18

Graphic Representation of the Equations :

    -3y + 6x = 8        7y + 4x = 18  

  
 

Solve by Substitution :

// Solve equation [2] for the variable  y 
 

  [2]    7y = -4x + 18

  [2]    y = -4x/7 + 18/7

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

   [1]    6x - 3•(-4x/7+18/7) = 8
   [1]    54x/7 = 110/7
   [1]    54x = 110

// Solve equation [1] for the variable  x 

   [1]    54x = 110 

   [1]    x = 55/27 

// By now we know this much :

    x = 55/27
    y = -4x/7+18/7

// Use the  x  value to solve for  y 

    y = -(4/7)(55/27)+18/7 = 38/27 

Solution :

 {x,y} = {55/27,38/27}