\( \begin{array}{l} \text { 10) }-5 x+y=-3 \\ 3 x-8 y=24\end{array} \)

To tackle the system of equations, we can use substitution or elimination. Let’s choose elimination for a fun twist! First, we can rearrange the first equation to isolate \(y\): \(y = 5x - 3\). Now, substitute this into the second equation: \[ 3x - 8(5x - 3) = 24 \] Expanding gives us \(3x - 40x + 24 = 24\), which simplifies to \(-37x + 24 = 24\). Solving for \(x\), we find \(x = 0\). Plugging \(x\) back into our expression for \(y\) gives \(y = -3\). So the solution is \( (0, -3) \)! As a refreshing idea, always double-check your answer by substituting back into the original equations to ensure both sides match up perfectly. It's like a math dance, and you want everyone to be in sync!