Question 1182942
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Note that if you were to receive 10 solutions from 10 different tutors, they would probably be all different.<br>
The solution from the other tutor is fine.<br>
I personally would work as much of the problem as I could without introducing fractions or decimals.  The method is straightforward; but it is aggravatingly easy to make simple arithmetic errors along the way, leading of course to wrong answers.  Avoiding fractions and decimals makes those sloppy errors less likely.<br>
Here is how I would solve the system.<br><pre>
Original system, directly from the given equations:

   4  -3   1   -8
  -2   1  -3   -4
   1  -1   2    3

Our first objective is to get a 1 in row 1 column 1.  Since we can move rows, and since one of the rows has a 1 in column 1, switch rows:

   1  -1   2    3
  -2   1  -3   -4
   4  -3   1   -8

The next objective is to get 0's in column1 in the other two rows.  The method for doing that is standard -- add appropriate multiples of row 1 to rows 2 and 3.

   1  -1   2    3
   0  -1   1    2   row 2, plus 2 times row 1
   0   1  -7  -20   row 3, minus 4 times row 1

Our next objective is to get a 1 in row 2 column 2.  We could do that by switching rows 2 and 3, or by multiplying row 2 by -1.  I arbitrarily chose the latter.

   1  -1   2    3
   0   1  -1   -2   row 2, multiplied by -1
   0   1  -7  -20

Next we use the 1 in row 3 column 3 to get 0's in column 2 in rows 1 and 3

   1   0   1   1   row 1, plus row 2
   0   1  -1  -2
   0   0  -6 -18   row 3, minus row 2

Now we want a 1 in row 3 column 3, so divide row 3 by -6

   1   0   1   1
   0   1  -1  -2
   0   0   1   3   row 3, divided by -6

And last we use the 1 in row 3 column 3 to get 0's in column 3 in rows 1 and 2

   1   0   0  -2  row 1, minus row 3
   0   1   0   1  row 3, plus row 3
   0   0   1   3</pre>

Solution: (-2,1,3)<br>