Question

2x+y+z=6
-3x-4y+2z=4
x+y-z=-2
solve the system of all variables using a matriz

Answer 1

+2 +1 +1 +6
-3 -4 +2 +4
+1 +1 -1 -2

+1 +1/2 +1/2 +3
-1 -4/3 +2/3 +4/3
+1 +1/1 -1/1 -2

+1 +1/2 +1/2 +3
+0 +2/3 +7/6 +13/3
+0 -1/2 +3/2 +5

+1 +1/2 +1/2 +3
+0 +1/1 +7/4 +13/2
+0 -1/2 +3/2 +5

+1 +1/2 +1/2 +3
+0 +1/1 +7/4 +13/2
+0 -1/2 +3/2 +5
(middle times 1/2--> 0 1/2 7/8 13/4 subtract from 1, add to 3 for new rows 1 and 3 )
+1 +0 -3/8 -1/4
+0 +1 +7/4 +13/2
+0 +0 19/8 +39/4

+1 +0 -3/8 -1/4
+0 +1 +7/4 +13/2
+0 +0 +1/1 +78/19
(row 3 times 7/4, subtract from row 2 for new row 2)
+1 +0 -3/8 -1/4
+0 +1 + 0 -13/19
+0 +0 +1/1 +78/19
(Row 3 times 3/8, add to row 1 for new row 1)

+1 +0 +0 +49/38
+0 +1 +0 -13/19
+0 +0 +1 +78/19

Answer 2

Damon, you must have made an arithmetic error somewhere, but I'm too lazy to find it, lol

here is my manipulation:

1 1 -1 -2
2 1 1 6
-3 -4 2 4 re-arranged the rows

=

1 1 -1 -2
0 1 -3 -10 did 2x#1 - #2
0 -1 -1 -2 did 3x#1 + #3

=
1 1 -1 -2
0 1 -3 -10
0 0 -4 -12 did #2 + #3

here we can stop, since line #3 says
-4z = -12
z = 3
now back in line 2
y - 3z = -10
y - 9 = -10
y = -1

and finally in #1 which says
x + y - z = -2
x - 1 - 3 = -2
x = 2

so x=2, y=-1, and z=3
which verifies in all 3 equations

Answer 3

+2 +1 +1 +6
-3 -4 +2 +4
+1 +1 -1 -2

+1 +1/2 +1/2 +3
-1 -4/3 +2/3 +4/3
+1 +1/1 -1/1 -2

+1 +1/2 +1/2 +3
+0 -5/6 +7/6 +13/3 correction
+0 -1/2 +3/2 +5

You will have to follow through with the correction