2x + 3y - 4z = 7
3x + 4y - 2z = 9
5x + 7y - 6z = 20
Use Row 1 to get a 0 where the 3 is in Row 2:
Multiply Row 1 by -3 and the Row 2 by 2
Add Row 1 to Row 2
Restore Row 1 as it was
Use Row 1 to get a 0 where the 5 is in Row 3
Multiply Row 1 by -5 and Row 3 by 2
Add Row 1 to Row 3
Restore Row 1 as it was:
Use Row 2 to get a 0 where the -1 is in Row 3
Multiply Row 2 by -1 and keep Row 3 as it is
Add Row 2 to Row 3
Oh oh! We can see there is no solution because
the bottom Row is an abbreviation for the equation:
0x + 0y + 0z = 8
There are no values of x,y, or z that we can substitute
for any of them that will make the left side equal to 8,
because the left side will always be 0 no matter what
numbers you substitute for the letters. Therefore there
is no solution and this is called an "inconsistent" system.
Edwin
