Solution - Linear equations with two unknowns

System of Linear Equations entered :

  [1]           14b+2a=52
  [2]           11a-56+38b

Equations Simplified or Rearranged :

   [1]    14b + 2a = 52
   [2]    38b + 11a = 56

Graphic Representation of the Equations :

    2a + 14b = 52        11a + 38b = 56  

  
 

Solve by Substitution :

// Solve equation [2] for the variable  a 
 

  [2]    11a = -38b + 56

  [2]    a = -38b/11 + 56/11

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

   [1]    14b + 2•(-38b/11+56/11) = 52
   [1]    78b/11 = 460/11
   [1]    78b = 460

// Solve equation [1] for the variable  b 

   [1]    78b = 460 

   [1]    b = 230/39 

// By now we know this much :

    b = 230/39
    a = -38b/11+56/11

// Use the  b  value to solve for  a 

    a = -(38/11)(230/39)+56/11 = -596/39 

Solution :

 {b,a} = {230/39,-596/39}