(1) 3x+6y-12z=36
(2) x+2y-4z=12
(3) 4x+8y-16z=48
The first equation (1) is the second equation (2) multiplied by 3:
(2) x+2y-4z=12→3(x+2y-4z=12)→3x+6y-12z=36 (1)
The third equation (3) is the second equation (2) multiplied by 4:
(2) x+2y-4z=12→4(x+2y-4z=12)→4x+8y-16z=48 (3)
The equations are linearly dependent, Then the system of equations is dependent, and then consistent too.
