Question

Solve the system by substitution. (Please Explain how you did it Ill give brainliest)

Answer 1

Answer:

{x,y,z} = {0,13,20}

Step-by-step explanation:

{x,y,z} = {0,13,20}  

 

System of Linear Equations entered :

  [1]    x + y - z = -7

  [2]    2x - y + z = 7

  [3]    x - 4y + 3z = 8

Solve by Substitution :

// Solve equation [3] for the variable  x  

 

 [3]    x = 4y - 3z + 8

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

  [1]    (4y-3z+8) + y - z = -7

  [1]    5y - 4z = -15

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

  [2]    2•(4y-3z+8) - y + z = 7

  [2]    7y - 5z = -9

// Solve equation [2] for the variable  y  

 

 [2]    7y = 5z - 9

 [2]    y = 5z/7 - 9/7

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

  [1]    5•(5z/7-9/7) - 4z = -15

  [1]     - 3z/7 = -60/7

  [1]     - 3z = -60

// Solve equation [1] for the variable  z  

  [1]    3z = 60  

  [1]    z = 20  

// By now we know this much :

   x = 4y-3z+8

   y = 5z/7-9/7

   z = 20

// Use the  z  value to solve for  y  

   y = (5/7)(20)-9/7 = 13  

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

 x = 4(13)-3(20)+8 = 0