SOLUTION: The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination. 2y + z = 9 x + y = 9 3x + 3y &#

Algebra ->  Matrices-and-determiminant -> SOLUTION: The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination. 2y + z = 9 x + y = 9 3x + 3y &#      Log On


   

Question 946271: The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination.

2y + z = 9
x + y = 9
3x + 3y − z = 10
Answer by MathLover1(20849) About Me  (Show Source):
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2y + z = 9
x + y = 9
3x + 3y − z = 10

0........... 2........... 1........... 9
1........... 1........... 0........... 9
3........... 3........... -1........... 10



Swapping row2 with row1

1........... 1........... 0........... 9
0........... 2........... 1........... 9
3........... 3........... -1........... 10

Add (-3 * row1) to row3


1........... 1........... 0........... 9
0........... 2........... 1........... 9
0........... 0........... -1........... -17

Divide row2 by 2
1........... 2........... 0........... 9
0........... 1........... 1/2........... 9/2
0........... 0........... -1........... -17

Divide row3 by -1

1........... 1........... 0........... 9
0........... 1........... 1/2........... 9/2
0........... 0........... 1........... 17

Add (-1/2 * row3) to row2

1........... 1........... 0........... 9
0........... 1........... 0........... -4
0........... 0........... 1........... 17

Add (-1 * row2) to row1

1........... 0........... 0........... 13
0........... 1........... 0........... -4
0........... 0........... 1........... 17



x=13
y=-4
z=17