Which classification best describes the following system of equations?

5x+10y+15z=60

2x+4y+6z=60

x+2y+3z=60

inconsistent and dependent

consistent and dependent

consistent and independent

inconsistent and independent

Inconsistent system of equation consists of equations whose graphs do not intersect (they are parallel lines) and there is no solution.
Dependent system of equations consists of equations that are same (their graph is the same) but written in different form.
Let us analyze the equations:
5x+10y+15z=60 (1)
2x+4y+6z=60 (2)
x+2y+3z=60   (3)
We can divide the first one by 5 to obtain the same left side as in equation (3), and to see if they are dependent:
x+2y+3z=12
which is not the same as x+2y+3z=60.
They are not dependent (they are independent).

We can divide the second one by 2 to obtain the same left side as in equation (3), and to see if they are dependent:
x+2y+3z=30 (2) divided by 2
which is not the same as x+2y+3z=60. They are not dependent (they are independent).

The graphs of the three functions are parallel so, they are inconsistent.
Solution: inconsistent and independent