Question

Solve the system of equations 2x+4y+3z=6 5x+8y+6z=4

Answer 1

Answer:Solution :

{x,y,z} = {-8,52/7,-18/7}  

 

System of Linear Equations entered :

  [1]    2x + 4y + 3z = 6

  [2]    5x + 8y + 6z = 4

  [3]    4x + 5y + 2z = 0

Solve by Substitution :

// Solve equation [3] for the variable  z  

 

 [3]    2z = -4x - 5y  

 [3]    z = -2x - 5y/2  

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

  [1]    2x + 4y + 3•(-2x-5y/2) = 6

  [1]    -4x - 7y/2 = 6

  [1]    -8x - 7y = 12

// Plug this in for variable  z  in equation [2]

  [2]    5x + 8y + 6•(-2x-5y/2) = 4

  [2]    -7x - 7y = 4

// Solve equation [2] for the variable  y  

 

 [2]    7y = -7x - 4

 [2]    y = -x - 4/7

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

  [1]    -8x - 7•(-x -4/7) = 12

  [1]    -x = 8

// Solve equation [1] for the variable  x  

  [1]    x = - 8  

// By now we know this much :

   x = -8

   y = -x-4/7

   z = -2x-5y/2

// Use the  x  value to solve for  y  

   y = -(-8)-4/7 = 52/7  

// Use the  x  and  y  values to solve for  z  

 z = -2(-8)-(5/2)(52/7) = -18/7  

Solution :

{x,y,z} = {-8,52/7,-18/7}  

Step-by-step explanation: