Linear equations with two unknowns

System of Linear Equations entered :

   [1]    4m - 3n = 3
   [2]    2m - 3n = 8

Graphic Representation of the Equations :

    -3n + 4m = 3        -3n + 2m = 8  

  
 

Solve by Substitution :

// Solve equation [2] for the variable  m 
 

  [2]    2m = 3n + 8

  [2]    m = 3n/2 + 4

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

   [1]    4•(3n/2+4) - 3n = 3
   [1]    3n = -13

// Solve equation [1] for the variable  n 

   [1]    3n = - 13 

   [1]    n = - 13/3 

// By now we know this much :

    m = 3n/2+4
    n = -13/3

// Use the  n  value to solve for  m 

    m = (3/2)(-13/3)+4 = -5/2 

Solution :

 {m,n} = {-5/2,-13/3}