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5 3 7 4
3 26 2 9
7 2 10 5
Multiply row 1 by 1/5:
1 3/5 7/5 4/5
3 26 2 9
7 2 10 5
Add -3 times row 1 to row 2:
1 3/5 7/5 4/5
0 121/5 -11/5 33/5
7 2 10 5
Add -7 times row 1 to row 3:
1 3/5 7/5 4/5
0 121/5 -11/5 33/5
0 -11/5 1/5 -3/5
Multiply row 2 by 5/121:
1 3/5 7/5 4/5
0 1 -1/11 3/11
0 -11/5 1/5 -3/5
Add -3/5 times row 2 to row 1:
1 0 16/11 7/11
0 1 -1/11 3/11
0 -11/5 1/5 -3/5
Add 11/5 times row 2 to row 3:
1 0 16/11 7/11
0 1 -1/11 3/11
0 0 0 0
This is as far as we can go. This translates into:
x + (16/11)z = 7/11 or x = (-16/11)z + 7/11
y - (1/11)z = 3/11 or y = (1/11)z + 3/11
So there are an infinite number of solutions. One way to express the solution would be:
((-16/11)z + 7/11, (1/11)z + 3/11, z) where z is any real number.
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