7. \( \left\{\begin{array}{l}x-3 y=-24 \\ 5 x+8 y=-5\end{array}\right. \)

To solve the system of equations, let's first express the first equation in terms of \(x\): 1. From \(x - 3y = -24\), we can rewrite it as \(x = 3y - 24\). Now, substitute \(x\) in the second equation: 2. Substitute into \(5x + 8y = -5\): \[ 5(3y - 24) + 8y = -5 \\ 15y - 120 + 8y = -5 \\ 23y - 120 = -5 \\ 23y = 115 \\ y = 5 \] Now, substitute \(y\) back to find \(x\): 3. Using \(y = 5\) in \(x = 3y - 24\): \[ x = 3(5) - 24 = 15 - 24 = -9 \] Thus, the solution to the system is \(x = -9\) and \(y = 5\). The solution is \((x, y) = (-9, 5)\).