SOLUTION: x+y+z-w=5 2x+y-z+w=6 x-5y+3z+w=9 -x-y+z+4w=7 These always confuse me.

Question 907712: x+y+z-w=5
2x+y-z+w=6
x-5y+3z+w=9
-x-y+z+4w=7
These always confuse me.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
1,1,1,-1,5
2,1,-1,1,6
1,-5,3,1,9
-1,-1,1,4,7

add down (-2) *row 1 to row 2
1,1,1,-1,5
0,-1,-3,3,-4
1,-5,3,1,9
-1,-1,1,4,7
add down (-1) *row 1 to row 3
1,1,1,-1,5
0,-1,-3,3,-4
0,-6,2,2,4
-1,-1,1,4,7
add down (1) *row 1 to row 4
1,1,1,-1,5
0,-1,-3,3,-4
0,-6,2,2,4
0,0,2,3,12
divide row 2 by -1
1,1,1,-1,5
0,1,3,-3,4
0,-6,2,2,4
0,0,2,3,12
add down (6) *row 2 to row 3
1,1,1,-1,5
0,1,3,-3,4
0,0,20,-16,28
0,0,2,3,12
add down (0) *row 2 to row 4
1,1,1,-1,5
0,1,3,-3,4
0,0,20,-16,28
0,0,2,3,12
divide row 3 by 20
1,1,1,-1,5
0,1,3,-3,4
0,0,1,-16/20,28/20
0,0,2,3,12
add down (-2) *row 3 to row 4
1,1,1,-1,5
0,1,3,-3,4
0,0,1,-4/5,7/5
0,0,0,23/5,46/5
divide row 4 by 23/5
1,1,1,-1,5
0,1,3,-3,4
0,0,1,-4/5,7/5
0,0,0,1,2
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (4/5) *row 4 to row 3
1,1,1,-1,5
0,1,3,-3,4
0,0,1,0,3
0,0,0,1,2
add up (3) *row 4 to row 2
1,1,1,-1,5
0,1,3,0,10
0,0,1,0,3
0,0,0,1,2
add up (1) *row 4 to row 1
1,1,1,0,7
0,1,3,0,10
0,0,1,0,3
0,0,0,1,2
add up (-3) *row 3 to row 2
1,1,1,0,7
0,1,0,0,1
0,0,1,0,3
0,0,0,1,2
add up (-1) *row 3 to row 1
1,1,0,0,4
0,1,0,0,1
0,0,1,0,3
0,0,0,1,2
add up (-1) *row 2 to row 1
1,0,0,0,3
0,1,0,0,1
0,0,1,0,3
0,0,0,1,2
final
1,0,0,0,3
0,1,0,0,1
0,0,1,0,3
0,0,0,1,2
"3","1","3","2"
(3,1,3,2)

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