SOLUTION: What is the solution set: 2x+6y-z=6 4x-3y+5z=-5 6x+9y-2z=11 Thank you and Merry Christmas!

Question 690540: What is the solution set:
2x+6y-z=6
4x-3y+5z=-5
6x+9y-2z=11
Thank you and Merry Christmas!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
2x+6y-z=6
4x-3y+5z=-5
6x+9y-2z=11

in matrix form is

$\begin{bmatrix} 2 & 6 & -1 & 6\\ 4 & -3 & 5 & -5\\ 6 & 9 & -2 & 11 \end{bmatrix}$

Now use row reduction to get
(Solution below provided by the Linear Algebra Toolkit)

(Solution above provided by the Linear Algebra Toolkit)

Since the last column is 1/2, 2/3, and -1, this means that , , and

The solution as an ordered triple is $\left(\frac{1}{2}, \frac{2}{3}, -1 \right )$
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