Question

What are the values of x, y, and z in this system of equations?

Answer 1

Answer:

{x,y,z}={5,−3,3}

Step-by-step explanation:

  [1]    2x + 4y + z = 1

  [2]    x - 2y - 3z = 2

  [3]    x + y - z = -1

// Solve equation [3] for the variable  y  

 [3]    y = -x + z - 1

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

  [1]    2x + 4•(-x +z -1) + z = 1

  [1]    -2x + 5z = 5

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

  [2]    x - 2•(-x +z -1) - 3z = 2

  [2]    3x - 5z = 0

// Solve equation [2] for the variable  x  

 [2]    3x = 5z

 [2]    x = 5z/3

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

  [1]    -2•(5z/3) + 5z = 5

  [1]    5z/3 = 5

  [1]    5z = 15

// Solve equation [1] for the variable  z  

  [1]    5z = 15

  [1]    z = 3

// By now we know this much :

   x = 5z/3

   y = -x+z-1

   z = 3

// Use the  z  value to solve for  x  

   x = (5/3)(3) = 5

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

 y = -(5)+(3)-1 = -3

Solution :

{x,y,z} = {5,-3,3}