What is the solution to this system of linear equations 3x 2y 14 5x y 32

Substitution method :

The equations are

Solve for y.

Substitute the values

Substitute the values

The solution of the system is

System of Linear Equations entered :

   [1]    3x - 2y = 14
   [2]    5x - y = 32

Graphic Representation of the Equations :

    -2y + 3x = 14        y + 5x = 32  

  
 

Solve by Substitution :

// Solve equation [2] for the variable  y 
 

  [2]    y = 5x - 32

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

   [1]    3x - 2•(5x-32) = 14
   [1]    -7x = -50

// Solve equation [1] for the variable  x 

   [1]    7x = 50 

   [1]    x = 50/7 

// By now we know this much :

    x = 50/7
    y = 5x-32

// Use the  x  value to solve for  y 

    y = 5(50/7)-32 = 26/7 

Solution :

 {x,y} = {50/7,26/7} 

System of Linear Equations entered :

   [1]    3x - 2y = 14
   [2]    5x + y = 32

Graphic Representation of the Equations :

    -2y + 3x = 14        y + 5x = 32  

  
 

Solve by Substitution :

// Solve equation [2] for the variable  y 
 

  [2]    y = -5x + 32

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

   [1]    3x - 2•(-5x+32) = 14
   [1]    13x = 78

// Solve equation [1] for the variable  x 

   [1]    13x = 78 

   [1]    x = 6 

// By now we know this much :

    x = 6
    y = -5x+32

// Use the  x  value to solve for  y 

    y = -5(6)+32 = 2 

Solution :

 {x,y} = {6,2} 

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