Question 904087
How he solved to get the answer he would know better than anyone else.  More than one way to do it.


{{{(matrix(3,4,
1,1,1,9,
2,4,2,14,
-1,8,-3,-39
))}}}


Simplify the second equation with the "14";


{{{(matrix(3,4,
1,1,1,9,
1,2,1,7,
-1,8,-3,-39
))}}}


Add R1 to R3 for new R3;


{{{(matrix(3,4,
1,1,1,9,
1,2,1,7,
0,9,-2,-30
))}}}


Revise R2 as R2-R1;


{{{(matrix(3,4,
1,1,1,9,
0,1,0,-2,
0,9,-2,-30
))}}}


The y variable is now solved as found in the second row, that y=-2.  

Re-order the rows:


{{{(matrix(3,4,
1,1,1,9,
0,9,-2,-30,
0,1,0,-2
))}}}


Revise R2 as  R2-9*R3;


{{{(matrix(3,4,
1,1,1,9,
0,0,-2,-12,
0,1,0,-2
))}}}


Revise R2 as -(1/2)*R2;


{{{(matrix(3,4,
1,1,1,9,
0,0,1,6,
0,1,0,-2
))}}}


That row 2 now shows {{{highlight(z=6)}}}.
And you also know {{{highlight(y=-2)}}}.


Avoiding further matrix operations, the Row 1 is {{{x+y+z=9}}}
{{{x=9-y-z}}}
{{{x=9+2-6}}}
{{{x=9-4}}}
{{{highlight(x=5)}}};

Solved for x, y, and z to the same values as your professor found.