Solution - Linear equations with two unknowns

System of Linear Equations entered :

   [1]    5x + 14y = -5
   [2]    -3x + 10y = 72

Graphic Representation of the Equations :

    14y + 5x = -5        10y - 3x = 72  

  
 

Solve by Substitution :

// Solve equation [2] for the variable  y 
 

  [2]    10y = 3x + 72

  [2]    y = 3x/10 + 36/5

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

   [1]    5x + 14•(3x/10+36/5) = -5
   [1]    46x/5 = -529/5
   [1]    46x = -529

// Solve equation [1] for the variable  x 

   [1]    46x = - 529 

   [1]    x = - 23/2 

// By now we know this much :

    x = -23/2
    y = 3x/10+36/5

// Use the  x  value to solve for  y 

    y = (3/10)(-23/2)+36/5 = 15/4 

Solution :

 {x,y} = {-23/2,15/4}