Question

. Solve the system of equations using the Elimination Method.

Answer 1

Answer:

{x,y,z}={1,3,4}

Step-by-step explanation:

System of Linear Equations given :

 [1]    x + 3y - 2z = 2

  [2]    3x + 2y + z = 13

  [3]    -2x + 3y - 3z = -5

Solve by Substitution :

// Solve equation [2] for the variable  z

 [2]    z = -3x - 2y + 13

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

  [1]    x + 3y - 2•(-3x-2y+13) = 2

  [1]    7x + 7y = 28

// Plug this in for variable  z  in equation [3]

  [3]    -2x + 3y - 3•(-3x-2y+13) = -5

  [3]    7x + 9y = 34

// Solve equation [3] for the variable  y

 [3]    9y = -7x + 34

 [3]    y = -7x/9 + 34/9

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

  [1]    7x + 7•(-7x/9+34/9) = 28

  [1]    14x/9 = 14/9

  [1]    14x = 14

// Solve equation [1] for the variable  x

  [1]    14x = 14

  [1]    x = 1

// By now we know this much :

   x = 1

   y = -7x/9+34/9

   z = -3x-2y+13

// Use the  x  value to solve for  y

   y = -(7/9)(1)+34/9 = 3

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

 z = -3(1)-2(3)+13 = 4

Solution :

{x,y,z} = {1,3,4}