Use elimination to solve the system of equations. Identify the system as consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent. \[ \begin{array}{l} 5 x+y=-12 \\ 7 x-3 y=-30 \end{array} \]

Step 1 ：Given the system of equations: \[\begin{array}{l} 5x+y=-12 \\ 7x-3y=-30 \end{array}\]

Step 2 ：First, we make the coefficients of y the same in both equations. This can be achieved by multiplying the first equation by 3 and the second equation by 1.

Step 3 ：Then, we subtract the second equation from the first to eliminate y.

Step 4 ：We solve for x and find that \(x = -3\).

Step 5 ：Substitute \(x = -3\) into one of the original equations to solve for y. We find that \(y = 3\).

Step 6 ：Since we get a valid solution, the system is consistent.

Step 7 ：We check if the equations are dependent or independent by checking if one equation can be obtained from the other by multiplying it with a constant.

Step 8 ：Since one equation cannot be obtained from the other by multiplying it with a constant, the equations are independent.

Step 9 ：Final Answer: The system of equations is consistent and the equations are independent. The solution to the system of equations is \(\boxed{x = -3, y = 3}\).