x y 5z 1 6x 5y 28z 3 2x 3y 12z 5Solutionx y z 1 6x

x + y - 5z = 1 -6x - 5y + 28z = 3 2x + 3y - 12z = 5

x+ y -z = 1

-6x -5y +28z =3

2x +3y -12z = 5

Multiply first equation by 6 and add the result to the second equation. The result is:

x+ y -z = 1

y- 2z = 9

2x +3y -12z = 5

Multiply first equation by 2 and add the result to the third equation. The result is:

x+ y -z = 1

y- 2z = 9

y -2z =3

Multiply second equation by 1 and add the result to the third equation. The result is

x+ y-5z = 1

y- 2z = 9

0 = -6

the last equation is not possible. So the system has no solutions, it is inconsistent