$\begin{aligned} 4 x-9 y-4 z & =-59 \\ -7 x+5 y+z & =0.5 \\ -3 x-4 y-3 z & =-57.5\end{aligned}$

Step 1 ：We are given a system of linear equations with three variables: \(4x - 9y - 4z = -59\), \(-7x + 5y + z = 0.5\), and \(-3x - 4y - 3z = -57.5\).

Step 2 ：We can solve this system using various methods such as substitution, elimination or matrix method.

Step 3 ：Let's represent the system of equations in matrix form. The coefficient matrix A is \(\begin{bmatrix} 4 & -9 & -4 \\ -7 & 5 & 1 \\ -3 & -4 & -3 \end{bmatrix}\) and the constant matrix b is \(\begin{bmatrix} -59 \\ 0.5 \\ -57.5 \end{bmatrix}\).

Step 4 ：We solve for the variable matrix x which gives us the values of x, y, and z that satisfy all three equations simultaneously.

Step 5 ：The solution to the system of equations is \(x = 8.06458538e+14\), \(y = 1.75954590e+15\), and \(z = -3.15251974e+15\).

Step 6 ：Final Answer: The solution to the system of equations is \(\boxed{x = 8.06458538e+14, y = 1.75954590e+15, z = -3.15251974e+15}\).