Solution - Linear equations with two unknowns

System of Linear Equations entered :

   [1]    8x - 3y = -9
   [2]    5x - 4y = 12

Graphic Representation of the Equations :

    -3y + 8x = -9        -4y + 5x = 12  

  
 

Solve by Substitution :

// Solve equation [2] for the variable  x 
 

  [2]    5x = 4y + 12

  [2]    x = 4y/5 + 12/5

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

   [1]    8•(4y/5+12/5) - 3y = -9
   [1]    17y/5 = -141/5
   [1]    17y = -141

// Solve equation [1] for the variable  y 

   [1]    17y = - 141 

   [1]    y = - 141/17 

// By now we know this much :

    x = 4y/5+12/5
    y = -141/17

// Use the  y  value to solve for  x 

    x = (4/5)(-141/17)+12/5 = -72/17 

Solution :

 {x,y} = {-72/17,-141/17}